project submission

#Loading the Dataset

#Data Description

#The dataset consists of 14710 observations and 8 variables. Each row in dataset represents an employee; each column contains employee attributes:

#Independent Variables were: #Age: Age of employees, #Department: Department of work, #Distance from home, #Education: 1-Below College; 2-College; 3-Bachelor; 4-Master; 5-Doctor; #Education Field #Environment Satisfaction: 1-Low; 2-Medium; 3-High; 4-Very High; #Job Satisfaction: 1-Low; 2-Medium; 3-High; 4-Very High; #Marital Status, #Monthly Income, #Num Companies Worked: Number of companies worked prior to IBM, #Work Life Balance: 1-Bad; 2-Good; 3-Better; 4-Best; #Years At Company: Current years of service in IBM #Dependent Variable was: #Attrition: Employee attrition status(0 or 1)

library(readr)
library(MVA)

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library(HSAUR2)
library(SciViews)
library(scatterplot3d)
library(car)

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library(lattice)
library(GGally)

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library(ggplot2)
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library(ggvis)

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library(ggthemes)
library(cowplot)

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library(gapminder)
library(gganimate)

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library(tidyverse)

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library(gridExtra)

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library(factoextra)

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(FactoMineR)
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library(psych)

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library(NbClust)
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library(relaimpo)

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library(pROC)

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library(caTools)

attr <- read_csv("/Users/meet/Desktop/Attrition Data copy.csv")

## Rows: 1470 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (4): Department, MaritalStatus, EducationField, Attrition
## dbl (10): Sr.no, Education, DistanceFromHome, EnvironmentSatisfaction, JobSa...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

attr_new <- attr[,c(6:14)]
str(attr_new)

## tibble [1,470 × 9] (S3: tbl_df/tbl/data.frame)
##  $ Education              : num [1:1470] 2 1 2 4 1 2 3 1 3 3 ...
##  $ DistanceFromHome       : num [1:1470] 1 8 2 3 2 2 3 24 23 27 ...
##  $ EnvironmentSatisfaction: num [1:1470] 2 3 4 4 1 4 3 4 4 3 ...
##  $ JobSatisfaction        : num [1:1470] 4 2 3 3 2 4 1 3 3 3 ...
##  $ Age                    : num [1:1470] 41 49 37 33 27 32 59 30 38 36 ...
##  $ MonthlyIncome          : num [1:1470] 5993 5130 2090 2909 3468 ...
##  $ NumCompaniesWorked     : num [1:1470] 8 1 6 1 9 0 4 1 0 6 ...
##  $ WorkLifeBalance        : num [1:1470] 1 3 3 3 3 2 2 3 3 2 ...
##  $ YearsAtCompany         : num [1:1470] 6 10 0 8 2 7 1 1 9 7 ...

corrplot(cor(attr_new), type = "upper", method = "color")

#The correlation matrix shows us that there is correlation between the columns in both cases.
#Hence, Principal Component Analysis (PCA) can be used to reduce the number of columns for the analysis.

result<-cor(attr_new)
result 

##                            Education DistanceFromHome EnvironmentSatisfaction
## Education                1.000000000      0.021041826            -0.027128313
## DistanceFromHome         0.021041826      1.000000000            -0.016075327
## EnvironmentSatisfaction -0.027128313     -0.016075327             1.000000000
## JobSatisfaction         -0.011296117     -0.003668839            -0.006784353
## Age                      0.208033731     -0.001686120             0.010146428
## MonthlyIncome            0.094960677     -0.017014445            -0.006259088
## NumCompaniesWorked       0.126316560     -0.029250804             0.012594323
## WorkLifeBalance          0.009819189     -0.026556004             0.027627295
## YearsAtCompany           0.069113696      0.009507720             0.001457549
##                         JobSatisfaction          Age MonthlyIncome
## Education                  -0.011296117  0.208033731   0.094960677
## DistanceFromHome           -0.003668839 -0.001686120  -0.017014445
## EnvironmentSatisfaction    -0.006784353  0.010146428  -0.006259088
## JobSatisfaction             1.000000000 -0.004891877  -0.007156742
## Age                        -0.004891877  1.000000000   0.497854567
## MonthlyIncome              -0.007156742  0.497854567   1.000000000
## NumCompaniesWorked         -0.055699426  0.299634758   0.149515216
## WorkLifeBalance            -0.019458710 -0.021490028   0.030683082
## YearsAtCompany             -0.003802628  0.311308770   0.514284826
##                         NumCompaniesWorked WorkLifeBalance YearsAtCompany
## Education                      0.126316560     0.009819189    0.069113696
## DistanceFromHome              -0.029250804    -0.026556004    0.009507720
## EnvironmentSatisfaction        0.012594323     0.027627295    0.001457549
## JobSatisfaction               -0.055699426    -0.019458710   -0.003802628
## Age                            0.299634758    -0.021490028    0.311308770
## MonthlyIncome                  0.149515216     0.030683082    0.514284826
## NumCompaniesWorked             1.000000000    -0.008365685   -0.118421340
## WorkLifeBalance               -0.008365685     1.000000000    0.012089185
## YearsAtCompany                -0.118421340     0.012089185    1.000000000

#Principal Component Analysis
attr_pca <- prcomp(attr_new,scale=TRUE)
attr_pca

## Standard deviations (1, .., p=9):
## [1] 1.4107854 1.0961163 1.0284243 1.0017232 0.9918265 0.9858032 0.9380353
## [8] 0.7089431 0.6395853
## 
## Rotation (n x k) = (9 x 9):
##                                   PC1         PC2          PC3         PC4
## Education                2.381768e-01 -0.35557851 -0.197280301  0.09516238
## DistanceFromHome        -8.671733e-03  0.06435091 -0.514604455  0.57141436
## EnvironmentSatisfaction -9.815712e-05 -0.01048877  0.543287792 -0.07285182
## JobSatisfaction         -2.501490e-02  0.19635694 -0.243998413 -0.73787765
## Age                      5.648580e-01 -0.17188575 -0.031031680 -0.07449252
## MonthlyIncome            5.879270e-01  0.18877561  0.051145765 -0.01437114
## NumCompaniesWorked       2.352160e-01 -0.70653759  0.053680763 -0.10519118
## WorkLifeBalance          1.281059e-02  0.06095915  0.578824064  0.30375136
## YearsAtCompany           4.715480e-01  0.51250805  0.008252963  0.07465387
##                                  PC5          PC6        PC7         PC8
## Education                0.147310191  0.380586266  0.7648985  0.10135538
## DistanceFromHome        -0.413127157  0.387344497 -0.2884104  0.01656602
## EnvironmentSatisfaction -0.792975712  0.147162364  0.2195899  0.01206021
## JobSatisfaction         -0.038278906  0.572850578 -0.1554622  0.05360003
## Age                     -0.063514430  0.001825971 -0.1136350 -0.73608470
## MonthlyIncome            0.005456455 -0.070320656 -0.1458130  0.12629670
## NumCompaniesWorked      -0.056606187 -0.021737738 -0.3990416  0.48889329
## WorkLifeBalance          0.412404321  0.586824005 -0.2253115 -0.04159593
## YearsAtCompany           0.002113045 -0.074300192  0.1232388  0.43349260
##                                 PC9
## Education               -0.08349607
## DistanceFromHome        -0.01693693
## EnvironmentSatisfaction -0.02425999
## JobSatisfaction          0.01245128
## Age                      0.29344102
## MonthlyIncome           -0.75742732
## NumCompaniesWorked       0.17205718
## WorkLifeBalance          0.04338735
## YearsAtCompany           0.54836854

summary(attr_pca)

## Importance of components:
##                           PC1    PC2    PC3    PC4    PC5    PC6     PC7
## Standard deviation     1.4108 1.0961 1.0284 1.0017 0.9918 0.9858 0.93804
## Proportion of Variance 0.2212 0.1335 0.1175 0.1115 0.1093 0.1080 0.09777
## Cumulative Proportion  0.2212 0.3546 0.4722 0.5837 0.6930 0.8009 0.89870
##                            PC8     PC9
## Standard deviation     0.70894 0.63959
## Proportion of Variance 0.05584 0.04545
## Cumulative Proportion  0.95455 1.00000

#Scree diagram
fviz_eig(attr_pca, addlabels = TRUE)

# The scree diagram shows us that sum of the first 2 principal components is less than 70%.
# So, we cannot move forward using PCA for column reduction.
# We now move on to check EFA for this main dataset.


pca_data <- as.data.frame(attr_pca$x)
pca_data <- pca_data[,1:2]

#Exploratory Factor Analysis (EFA)
fit.attr <- principal(attr[,6:14], nfactors=5, rotate="varimax")
fa.diagram(fit.attr)

# Defining the factors obtained

# RC1
# All of them YearsAtCompany, MonthlyIncome and Age are popular factors among all employees in terms of attrition.

# RC2
# NumCompaniesWorked and Education are popular factors.

# RC3
# It has only 1 factor DistanceFromHome

# RC4
# Both factors JobSatisfaction and WorkLifeBalance are important in terms of attrition for employees

# RC5
# RC5 has only one variable, Enviornment Satisfaction.

# Defining new columns through EFA

efa_data <- as.data.frame(fit.attr$scores)
efa_data

##               RC1          RC2           RC4          RC3           RC5
## 1    -0.417720371  1.420684382 -2.6196400200 -0.669024391 -0.0639742397
## 2     0.590433801 -0.815885321  0.5428254314 -0.115196832  0.6302573269
## 3    -1.156384919  0.694986263 -0.0622469420 -1.167435276  1.4640304453
## 4    -0.246767057 -0.337471126  0.1057013656 -0.622696488  0.7333091064
## 5    -1.436474293  0.869471891  0.6333471330 -1.145848511 -0.8327594849
## 6    -0.306523556 -1.263860792 -1.5754649157 -0.659057596  1.1588009984
## 7    -0.407765702  1.702249017  0.1884392202  0.099862209  0.5532967795
## 8    -0.888319480 -1.319977699  0.0429559225  1.300085494  1.4119239983
## 9     0.726937482 -0.837508813  0.1106768804  1.415601272  0.9597903899
## 10   -0.351744429  0.873980567 -0.8439631970  2.099078463  0.4422761251
## 11   -0.492509995 -0.602149493  0.7346274232  0.902709119 -1.6618589133
## 12   -0.070091733 -1.547233238  0.1037839246  0.525189210  1.1016490751
## 13   -0.627162329 -1.194609919 -0.8891879465  1.974204668 -1.1517957072
## 14   -0.631762262 -1.127165298 -0.6155303133  0.585105278 -0.6327836917
## 15   -1.028625081  0.278666178  0.1386493947  1.335234324  0.2687651726
## 16    0.380989017 -0.293026351  1.5320521291  1.765855782 -0.9422563891
## 17   -0.507431955 -0.919876982 -0.2569410317  0.131761085 -1.3912928620
## 18   -1.162360489 -1.153395426 -1.4811517968  0.754608888  1.1906202033
## 19    2.920207664  0.011946448 -0.6182992384 -1.069594386 -1.8222467339
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## 24   -1.385266113 -1.284852769 -0.5395200630  0.144759501  0.2231654969
## 25   -0.708141174 -0.715133185  1.2782321252 -0.139807732 -0.2244610261
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## 29    1.846513042  0.019154885 -0.5587079072 -0.549502758 -1.8224393056
## 30    0.865163254  1.464352183  0.3712498398 -0.017086016 -0.6146976370
## 31   -1.018059407  0.296128835 -0.6368427209 -1.285263029  0.2094997409
## 32    0.172020498  0.227461082  0.3167976069 -0.748604908  0.7588313949
## 33   -0.216018289 -1.293120858  0.0736721826 -0.130037276  1.1398716805
## 34   -0.714760010  0.045755318  0.2740107452 -1.395650227  0.9913957405
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## 36   -0.279289523 -0.424758232 -1.0173097782 -0.450587734  1.3153401392
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## 86    0.518603781  1.059977956 -1.7157076894 -0.256560174  1.2934289914
## 87   -1.491651839 -0.709395888  1.3316454641 -0.606713714  0.6549353560
## 88   -0.167545781  0.869079062 -0.7001633338 -0.375092136  0.9138895975
## 89    0.061742228 -0.999494352 -0.5574882200 -1.089891084  0.0041916217
## 90    0.930069952 -0.687017093 -0.6990270000 -0.507398395  0.3416546731
## 91    2.012507249 -0.296856027 -0.1616858792 -0.065097285 -0.0206227396
## 92    0.688986401  0.187562402 -2.5120779514  2.006203004  0.0459330778
## 93    0.007531852 -0.998189200 -0.2202192530  0.058578418  0.3833095051
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## 99    3.997735085 -0.708858586 -0.8641202868  0.802068777  0.8066529308
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## 108  -0.398153113 -0.859783435  0.1312529581 -0.552054103  0.0461466356
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## 113   1.564977890  0.371975238 -0.6698594203  1.271869029  1.1546528094
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## 115  -1.001826037  1.426530553  0.7222421328 -0.321922940  0.1824921728
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## 117   0.711638913 -0.240284043  1.4066252446 -0.059707055  0.2159848843
## 118   0.677638734 -1.275836826 -0.6111632217 -0.267706412 -0.6389427538
## 119  -0.980622588  0.360265239 -0.7021913263 -1.351369130 -1.2643608470
## 120   2.985456689 -1.636104781  0.4088158783  0.908134091  0.2012218029
## 121  -0.285582872 -0.698576499 -0.7883597286  1.877778638 -1.6156938800
## 122   0.097224706 -1.349213805  1.6926655404  0.997918566  0.2230594875
## 123  -0.124738746  2.834301616  0.5818555578  0.410027270 -0.4392618216
## 124   2.506450443  1.195247253 -0.0008675197 -0.729338590 -1.2971968848
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## 126  -0.891886044 -0.544374555 -0.1733266775  0.333029715  0.1670966896
## 127   3.918999262 -0.748955575 -1.4786534376  1.938999196  0.8006642771
## 128  -1.487079964 -1.512667270 -0.8287611739  1.583873947  1.4328211340
## 129  -1.023200996 -1.912073008 -0.6149890482 -1.287818874  0.3803115660
## 130   1.031492333  0.318694524  0.4398407628  2.224257488  0.0940824352
## 131  -0.341841114  0.646219444  0.0368519269  1.735824582 -0.5572997310
## 132   0.251041728  0.886247346 -0.7203451814 -0.278343583  0.3288597597
## 133  -0.769010824  0.022067425  0.1046986492  0.922164138 -0.6746126985
## 134   0.481695686 -0.628568148 -0.0521438290 -0.384525811  0.6595512374
## 135  -0.418347352 -1.729908272  0.1073671031  1.451435591  0.4789433793
## 136  -0.737388478  0.711852015  0.6334176945 -0.505293812 -0.2620100464
## 137   0.655457422  0.781992586 -0.6837519108 -0.577013910 -1.7421758327
## 138   0.709875588  0.210388487  1.0344456235 -1.086822931  0.8061217278
## 139  -0.507770741 -0.410762884  0.1887165045  1.766601379 -1.6155691088
## 140   0.194796440 -0.937158200 -2.4188468108  0.655559129  0.1328240166
## 141  -0.812318840  1.069785412  2.3217278664 -0.345069247 -1.3834404066
## 142  -0.220568897  0.860060680 -1.5714193164  2.077993436  0.4066043293
## 143  -0.500214081  0.951607884  0.0826297082 -0.673751684  0.6715422471
## 144  -0.711651415 -0.469772195 -0.8255250458  1.297650379 -1.5951203380
## 145   0.092664550 -1.640193844  0.3459886340 -0.891851604  0.9996863060
## 146  -1.046319802  0.632242990  1.3769783303 -0.153399988  1.2288159272
## 147  -0.524687383 -1.716581377 -0.6657235759 -1.289890043 -0.4670346397
## 148   0.958752596  0.853361993  0.4112111423  0.817652441  1.3535181616
## 149  -0.471505051  0.553510715  1.3585367365  0.473738890  0.0417664381
## 150  -1.464630688 -1.490124617  0.7166087436 -0.694958887 -0.3874491563
## 151   1.199187786 -0.845063413  0.7956381754  2.058974125 -0.7624436840
## 152   0.328830019  0.195251692  0.7994436878 -0.518286170 -0.3079477988
## 153   0.001744429  0.323352596 -2.0262563530  0.397885046 -0.2620329923
## 154   0.196293142  1.618658151 -1.2308490585  0.943771132 -0.2396256237
## 155   0.412858038 -0.789271319 -0.5529397042 -0.529535924 -0.8329368027
## 156  -0.053939436 -1.658090352  0.0200140293 -1.089925659  1.3503946605
## 157  -0.056773336  0.947773116 -0.0512918269 -0.381309505 -0.8264849402
## 158  -0.335536229  1.584107894 -0.4415684625  0.444560302 -0.3619620419
## 159   0.664311407  1.441008460 -1.5345141449 -0.587382925  0.2357682580
## 160  -0.930668652  1.190054152  0.0597712162 -0.974694275  0.1193424710
## 161  -1.069199221 -1.707415120 -0.5646570559  0.492782436  0.4409610751
## 162  -1.490864879  1.024982139 -1.1456967872  0.944559616  1.3910116503
## 163  -0.752988134 -0.559318417 -2.4017702811  1.877656843  0.1966286562
## 164   0.678551136  0.672997362 -2.6535201091  1.951413270  0.6949315560
## 165  -1.137302041 -0.430154255 -0.8649861485 -0.297994422  0.1522575095
## 166   1.494164398  0.791497679  0.6312305978  0.133601783  0.3760066413
## 167  -0.164942597  0.377152164  0.0280720361  0.293888721 -1.4937441978
## 168   0.410435442 -0.633902171 -0.5445438913 -0.881546855 -0.8014868267
## 169   0.344633259  0.502686486  0.3490452553 -1.826736857 -1.8314540195
## 170  -0.652760279  0.665454277  0.1444408632 -0.339405435 -0.2517189065
## 171  -0.715205663 -0.794241904 -0.1417534631  1.541000344  0.1348214633
## 172  -1.364987312 -1.785901343  2.3150932373 -1.082755295  0.4042176998
## 173  -0.517817726  0.064321265 -0.2989492537 -0.149936973  1.4440603816
## 174  -0.080293596 -0.762114549  1.4393880310  0.490883542  0.1158719089
## 175  -0.124389554  0.348296251  2.1750234022 -0.828707023  0.5145044226
## 176  -0.180738996  1.386184013  1.1814832431  0.144435358  0.4581937715
## 177  -0.539633988 -0.982557312  0.3298253888 -1.601183474 -0.0762202705
## 178  -1.498962364 -0.795367818 -1.4666091196 -0.677558968 -0.8143301012
## 179   2.096215001 -0.953226139  1.3135515604 -0.439807830 -0.4980618138
## 180  -0.603837280 -0.732008142 -0.6819177208 -0.502451639  0.3073790535
## 181  -0.896941223  0.368950462 -0.6674903663 -0.529035757  0.8203515717
## 182  -0.738577271 -0.543104820  0.7239466461  1.959232667  1.2968865362
## 183  -0.424795625 -0.333530695 -0.2916714801  1.692639736 -0.3938184957
## 184  -0.215745198  0.584825583 -1.0450392298 -0.562028953  0.3216949570
## 185   0.123139322  0.002388620  1.1992149286  0.746804236  1.3843858208
## 186  -0.279901947 -0.638173127  0.7569557799  0.738282660  0.9947728426
## 187   2.535550967 -1.586017032  0.0178130219 -0.811414097  1.4128583419
## 188   2.827912810  1.800075130  0.7051700992  0.527328390  0.3367329359
## 189   0.527734428 -1.278977025 -0.9505159134 -0.542818497  1.4782598961
## 190   1.103034988  0.685079688  0.5936845048 -0.631955294  1.2240764569
## 191   4.103488252 -0.808261058  0.0960940900 -0.751515291 -0.1550959856
## 192  -0.678350888 -0.637640824 -0.1625626375  0.692373464  1.0431019606
## 193  -0.587907552 -0.159340941  0.0404682664  1.131147389 -0.4253605638
## 194  -0.311581627  0.270671063  0.2627610259 -1.187661388  1.0442699235
## 195   1.984288798  1.013443108 -0.6768630332 -1.565048635 -1.0686189674
## 196  -0.222105310 -0.175593089  0.4595796094  2.195044100 -0.6106639236
## 197  -0.520998809  0.667551014  0.6842805843 -0.774135822 -0.5506743383
## 198  -0.026128902 -0.368878611 -0.0015957522  1.012082174  0.4204760573
## 199  -0.803764922  2.234269490  0.0164141420 -1.136897311  1.1935726839
## 200  -0.022476725  0.199476631 -2.4444118485  2.655932458  1.2352756630
## 201  -1.131785692 -0.117187016  1.3035995898 -0.792753866  0.7700110970
## 202   0.609291394  0.162219851 -0.6264174492  0.653699404  0.8132979452
## 203  -0.292466901 -0.350004657  1.0548998164 -0.398454364  0.6793460400
## 204  -0.399996922  0.741607345  0.2804122459 -0.152078557  0.5598609324
## 205  -0.732191556  0.804265287  1.2994166669  2.064318165  0.0839200241
## 206   0.235333280 -0.845669903 -1.4135019724  2.013363581 -0.7622033793
## 207  -1.086515888 -0.677034642 -0.1484595584  0.241493745  1.0268431132
## 208  -0.171553968 -1.423785831 -0.6539366540  0.408805863 -0.3893414639
## 209  -0.831787369  2.777612549 -2.4805612065  0.435141498  1.1060265334
## 210  -0.008238591  2.109728590  1.2905419545 -0.627446514  1.2117533216
## 211   0.913655608 -0.516474560 -1.4444184640 -0.306175001  0.7674886995
## 212   0.439933324 -1.599026336  0.0247431163 -1.137130293  0.4863292762
## 213   0.199096800 -0.877780076  0.1774077827  1.044028417  0.9555898244
## 214   0.935081859  1.809966878 -1.2388056072  0.886542675 -0.5008626427
## 215  -0.935061064  0.548744335  1.3779806312 -0.344480499  1.2158242685
## 216   0.374881459  0.364719579 -0.6589879226 -0.898487792  1.1226442091
## 217  -0.520137064  1.032794118  0.5583593004  2.645362434  0.2301730993
## 218  -0.650544424 -0.827207088 -0.8637804040 -0.425334241  0.0875817268
## 219   1.375430030  0.477390803 -0.6333704376 -0.814755305  1.1876070289
## 220   0.380058804  0.621789595  1.2092316503 -0.268366568  1.2104998114
## 221   0.183538927  0.580355190  1.6162822322 -1.054006228  1.4625345412
## 222  -1.049225091  1.296848350  0.7281966577 -0.500923004  0.1596157288
## 223   0.961340210 -0.636779708 -0.5716228256 -0.230847833 -0.7973208431
## 224   1.249447967 -0.802899362 -0.8685546136 -0.241485771 -1.6379863771
## 225  -0.385059891 -0.488027319  0.1077947935 -0.856015527 -0.1867615542
## 226  -0.185673690  0.968890810 -0.8366207892 -1.160093295  0.3062412445
## 227  -0.235218801  0.532263790 -0.5880066109 -0.958221010 -1.7762165186
## 228   0.382951964 -1.708356585 -0.6269926428 -1.423586113 -0.4374313522
## 229   0.603388783 -0.797533825  1.0091428056 -1.466178601  0.0070433292
## 230  -0.756080635 -1.374981461 -1.5601542729  0.885711672  0.5521968419
## 231  -0.531455765  1.878440905 -1.7360653634 -0.926354490  0.5408087606
## 232   2.804797697 -1.297643233 -0.6065406664 -1.000926924  0.2831949549
## 233  -0.514853980  2.136778308 -1.1679215616 -0.372502240  0.0038503293
## 234   1.631571284  1.024511375 -1.6120799255 -0.859999487  1.0260329152
## 235  -0.874572129  0.670825308 -2.4764270068  0.972781609  0.4120684977
## 236   1.913009800  0.257572975 -0.5754686941  0.216251837  1.1684226663
## 237  -0.596890633  0.575499987  2.2645843851 -1.133273912 -1.1919963054
## 238   3.995576318 -0.654754473  1.0382396354 -1.204989665 -1.9475519423
## 239  -0.623261697 -0.541587456  0.6739005884 -0.523072300  0.3904783240
## 240  -0.705547453 -0.450160932 -1.8415354734  0.039768473  1.0848055874
## 241  -0.920939119  1.673546036  0.0097495997 -1.133716842  0.1998307989
## 242  -0.417607133 -0.544741994 -0.4867685349  1.525338732 -0.1903640506
## 243  -0.770324154  0.123927396  0.3475048577  1.812459011  0.5845829909
## 244   0.134344181 -0.928363861 -0.6196132081  1.113234252 -1.4570719696
## 245   3.109271019 -1.154577651 -0.5873008737 -1.179549609  0.0240821735
## 246  -0.289080169  2.059011849  0.0932275690 -1.115553760 -0.5830963458
## 247  -0.792449468  0.005870949 -1.5177375302 -0.266943410 -0.0700436286
## 248  -0.060679560  1.091844658  1.4139039836 -0.378933807  1.0519091368
## 249  -0.679255175 -0.044395248  0.3324744475 -0.097378551  0.5415809785
## 250  -0.181780231  1.198283732 -0.0016898262 -0.458140785 -1.6501072584
## 251  -0.356629019  1.160297537  0.0233654646 -0.343721051 -1.3590320152
## 252   1.665937005 -0.750582937  0.1221366116 -0.684299147 -0.1881184232
## 253  -0.536294400 -0.875253813 -0.5337566816  0.270642511  0.0269234233
## 254  -0.209899380  0.168440366  1.2929204943  1.080365056  1.4343113981
## 255  -0.373635463 -0.873012210 -0.5637631258  0.633717350  1.2019870931
## 256  -0.631322230 -0.958277476  0.1096493478 -0.993348105 -1.7545879269
## 257   0.056911533 -0.476288518  1.3124624082 -0.232179007  1.0204596898
## 258   2.652642850 -1.405715284  0.0581771798 -0.954925193 -1.4904625661
## 259  -0.340549560  0.337912064 -1.7181212062 -0.805794963  0.2472496853
## 260  -0.373744454 -1.377382440  1.7162160909  1.752266652  0.2183275265
## 261  -0.756919715 -0.131777397 -1.1631471684  0.898909118 -0.5930153361
## 262   0.068430536 -0.462968194 -0.6773161504 -1.277777670  1.2574072857
## 263  -0.766751679 -0.419037820  1.2835937651 -0.576983404  1.6022081944
## 264   1.154363908  0.728424777 -0.3096206755 -0.292892172  0.4096351721
## 265  -1.279956422  0.516162244 -1.7878776390  0.073857959 -1.6760093874
## 266  -0.837005408 -0.014517992  0.7193983399 -0.746702404 -1.5713409604
## 267   0.142601126 -1.154571873 -0.5019488293  1.142264079 -0.8865583347
## 268  -0.667671742 -1.001970692  1.4009394857 -0.102950168 -0.5457412131
## 269   2.270495381 -1.454268898 -0.5976318546  0.775525234  0.2549713655
## 270   0.576184085 -1.265451926 -0.5732842037 -0.564154920  0.8480445810
## 271   4.289457830 -1.032702063  1.3582604175 -0.243279191  1.0140449321
## 272   1.082607916  0.438144576 -0.1847790154  2.785995633 -1.6635480500
## 273  -0.744444206 -0.724202792 -1.4946691260  0.132242868  0.9812719292
## 274  -0.100435657  0.494785320  0.3567655605 -1.259063200 -0.0694051103
## 275  -0.918220075 -1.454517344  1.0438231298 -1.324125341  1.0399484026
## 276   0.576567010  0.279049993 -0.5845829953 -1.328678544 -1.8211576287
## 277   0.132180063  1.299700562 -0.1833071974  1.720999829 -0.3368861516
## 278   0.039868339 -0.579118527  1.3158855829  0.083499738 -1.3542235845
## 279  -0.506809715 -0.378893713 -1.1217511275  0.262212557  0.2537398676
## 280   1.725449837  0.085064653 -0.4003888429 -0.291094083 -0.8992734892
## 281   1.312223454  1.334375184 -0.9854475644 -0.399957089  0.2079284807
## 282   1.203852944 -1.544419001 -0.0402433910 -1.056715139 -0.3798939800
## 283  -0.101175749 -1.162690749 -1.5403846517 -0.721372194 -0.5756598953
## 284   0.773793236  0.078462228 -0.7472406608  0.607215577 -0.3993515655
## 285  -0.656431385 -0.901737211  1.4086083882  0.501769900 -1.4065089306
## 286   0.601170249 -1.050271809 -0.5939879762 -1.110862364  0.8850299765
## 287  -0.690756272  0.766381597 -1.8825105475  2.358967175  1.3224857158
## 288  -0.712445633  2.018521738 -0.5721537875  0.852709098  1.1637867212
## 289  -1.066512618  0.043707056  0.8317196456  0.903530106 -1.8212043022
## 290  -0.547200265 -1.243361500 -0.5902325263 -0.561253232  1.1175376322
## 291   0.768183911  2.853379019  1.3045340151  0.147589364  0.4886705747
## 292  -0.237973511  0.323732357  0.6921301316 -0.591271501  0.2758785086
## 293  -0.932171592 -0.264130001 -0.2270672500  0.211503471  1.0883831782
## 294  -0.136329933 -0.673431254 -0.4870126871 -0.805466324  0.6660541715
## 295  -0.562341449 -0.287379674 -1.5710686180  0.071886450 -0.7189973974
## 296   1.875247865  0.121943784  1.7314689273  1.368609188  0.2636460432
## 297  -1.533638987 -0.882483808  0.1450294012 -0.777935505  0.0207487221
## 298   0.506487845 -0.721577624 -0.1715269480  1.439911486  0.1655898574
## 299  -0.787133922  0.734021002 -0.5663441870  0.500463797  0.0268388117
## 300  -0.057399697  1.268814986  0.5533162284 -0.774151004  1.3082240979
## 301   2.378316451 -0.441129089  0.7856658817 -0.447965954  0.7895944504
## 302  -1.523288303 -0.939486531  0.1675313346 -0.007118760  0.9034892889
## 303  -0.169034621 -1.257833862  1.4274037364  1.113275261 -0.5734306312
## 304  -0.153153915  0.140254087 -1.5120643052 -0.254663203 -0.6134768239
## 305   1.430126907 -1.025182947 -1.5324284463 -0.659941591  0.0712280744
## 306  -0.201943112  1.403093427  0.7963416227  1.604413611 -0.6575415275
## 307   0.326039043 -0.786516557 -0.8332867722  0.230332472  1.0124534203
## 308   0.786091593 -0.257579264  0.7319101809  1.623387153 -1.2709756131
## 309   0.473703519  0.975400764 -0.1079238938 -0.947539245  0.9434588433
## 310  -0.286743045 -0.599715920 -0.5360824320 -0.703770049 -0.2204388377
## 311  -0.734560054  0.331238460  1.3661397349 -0.495527445 -1.4839737392
## 312   1.551064252 -0.643957927  1.3689608021  0.313671032 -1.6094858410
## 313  -0.896058400 -0.154131021 -2.4545665240 -0.057078087 -0.0502644012
## 314   0.442124058  1.031395323  0.7824871261 -0.387425000  1.0342315719
## 315   2.303167753 -1.457441699  1.3590595287  0.378748690  0.5989637895
## 316   0.117572997 -0.329022659 -0.6074082256 -0.132756803 -0.1717123880
## 317   0.856456125  1.213484582 -0.1080003445 -1.380082095  0.7047855909
## 318   0.346171927  0.904162944 -0.3160658052  0.578693636  0.1407501242
## 319  -0.936093941 -0.461804794 -0.1884232170  0.215229073  0.1771458064
## 320   0.320575832 -1.185874645  0.7309839911  0.014033657  0.3055188185
## 321  -0.528778702 -0.779725690  0.0996942328 -0.852452735  0.9339997303
## 322  -0.066804489 -0.042813887 -0.5676256289 -0.716186894  1.0673111654
## 323  -0.595855405  1.396538504 -1.5134339773 -0.832094710 -1.5611150387
## 324  -1.088152630  0.895694523 -1.4962535408 -0.774355425 -1.6659916807
## 325   0.206569321 -1.426737544 -0.5158561918  1.599984045  1.1274906730
## 326   0.437399500 -1.165608891  0.0734835166 -0.421785287  0.2874453328
## 327   2.638074998 -1.371739327 -0.5775264502 -0.686948883  0.2736757060
## 328  -0.664514569  0.392036464 -1.0032082258 -0.513971964  1.4667420602
## 329  -0.325420306 -0.029034486 -1.5244857696  0.112649212 -0.6507922970
## 330   1.059883152  1.633881294  0.0456215412 -0.623660861  0.8167290794
## 331   0.439684603 -0.151721340  1.0032852220 -0.402762578 -0.1632675874
## 332  -0.344208125 -1.621607371  0.6788100521 -0.861140422  0.4817025039
## 333   0.093281863  1.230484631 -0.9709762251  1.534728823  1.0685595785
## 334  -0.430000342  2.200908677  0.3312250779  0.325996499  0.6839963555
## 335  -0.051335593  1.958825764 -0.6452998255 -0.667372288  1.1461209398
## 336  -0.047172667 -0.227590219 -1.6527579754 -0.955427439 -0.4279906229
## 337  -0.721296661 -0.023119417  0.5149742341  0.903047140 -0.8804259660
## 338  -0.612478543 -0.201404369 -0.4779470768 -0.218306693 -1.3151013436
## 339   0.144757295 -0.881818121  0.1104868811 -0.502707641  0.9340202732
## 340  -0.187733263 -0.372080492  0.8322052675  0.119736283 -1.0039023181
## 341  -0.329740940  0.779017901 -1.6241511649 -0.649467787  1.5433460635
## 342   1.101948556 -1.321951237 -0.6010253134  0.182070472  0.2493911070
## 343   0.307679291 -0.424218646 -1.4478199950 -0.005083032 -0.1098603701
## 344   0.044603350 -1.424014161  0.7020210102  0.083374377  1.4227117848
## 345   0.979973591 -0.694076615  0.8017482126 -0.092021202 -0.1645360846
## 346  -0.876756148 -1.611321472 -1.4862839450  1.742010165  0.5263506519
## 347  -0.281008718  1.115936703  0.6473579354 -0.371771699  1.3006440335
## 348  -0.612731259 -0.018768414 -0.1661268370 -0.983027172 -0.1618277915
## 349   0.660303404  0.950655893 -0.5253198768  1.050402008 -1.9648030518
## 350  -0.609010744 -0.501427544 -0.8657331340 -0.376307648  1.0329435028
## 351  -0.351259838 -1.130283236 -0.1106857418 -1.026471257  0.5261086854
## 352  -0.388530082 -0.606620655  0.7251721374 -0.561135717  0.1007054351
## 353   0.209568096  0.372704279 -1.9660812303  2.565344935 -0.8201431338
## 354  -0.187903727  0.507861484  1.3503497022 -0.021558378  0.3316227108
## 355  -0.892717382  0.403447103  1.0229365715  0.766723073  1.4071455315
## 356  -0.250360164 -0.900460645  0.1182385849 -0.958675204  0.0375514696
## 357  -0.313718053  0.832557898 -0.6561278025 -1.243942440 -1.7464917405
## 358  -1.191401431 -1.458097745  0.7037388441 -0.918766103 -1.2634230511
## 359  -0.523385929  1.143453473 -0.5720035673 -1.233557070  0.6862448170
## 360   0.727467532  0.381149229 -0.5509613875 -1.085796338 -1.7798232390
## 361   0.380241899  1.033144855 -0.1061577755 -0.973991733  0.9511027344
## 362  -0.285913280  0.446192195  0.0606028646  0.039060186  0.8772204729
## 363  -1.124639754 -1.153763540 -1.4900247180 -0.033758977 -1.4654750743
## 364  -0.828423547 -0.414440507  0.0411365295 -0.559713631  0.9840448575
## 365  -0.707020387  1.077409274  1.3427300370  0.331875434  0.4331033936
## 366  -0.201861425  0.564726528  0.9328120452 -0.837406855 -0.0614613195
## 367   0.524788413 -0.167268617  0.6742176931 -0.454972919 -1.5812940326
## 368   0.437971292  1.298158310 -0.7206797570 -0.541408764  1.2967405157
## 369   0.104425855 -0.478109659  0.0240990646  1.120502639  0.4087686273
## 370  -0.827686609 -0.293887730  0.7742056219  0.257608378 -0.1333090565
## 371  -1.261621133 -0.731425856  0.8145857950  0.451264290  0.0818840822
## 372  -1.239508534  1.255466789 -0.5454805855  0.811690185  1.3125913067
## 373  -0.947677824  2.242208260  0.7190539041 -0.134907236  0.3421432424
## 374  -0.633305155 -1.047903165  0.7118025429 -0.770163888  1.1847397250
## 375  -0.240191350 -0.510106778 -0.4941176605 -0.318098907 -1.0722504341
## 376   0.330439161  1.919009929 -0.0671814239 -0.703049301 -0.3357009161
## 377   0.226720996  0.463074008 -1.6965609495  0.416465702  0.5956818211
## 378  -0.864395161  0.430879542  0.0022484459 -0.987231172  1.1379520012
## 379  -0.698668386  1.392667058 -1.5273177210  0.837049064 -1.2627289113
## 380   1.468270893  0.509773707 -0.7560861362 -1.309903594  0.2617741632
## 381  -0.558353988 -0.706605936  1.1348569516 -0.393332799  0.6248427582
## 382  -1.014061347 -1.117618213  0.6295619091 -0.799346184  0.5546546588
## 383  -0.643431497 -1.627941659  1.3477606129 -0.338721818  0.5005699467
## 384  -1.230451395 -0.670509632  0.8051390890  0.315337524 -1.6759470920
## 385   0.435150103 -0.946621956  0.0143762175 -0.970070262 -0.5708476230
## 386  -1.422092557  1.469233086 -0.6227494616 -1.259989260  0.4356382162
## 387   0.587125106 -0.653558354  0.4805709366  1.583067865  1.0900238818
## 388  -0.402854944  0.978064318  0.5979228423 -0.922240433  1.5548071723
## 389  -0.500630911  0.908201635  1.3221343370 -0.444459789 -0.7873429544
## 390  -0.769711621  0.651321110 -0.2228140612  0.748464094  0.0899952243
## 391   2.500791014 -0.807438985  0.7673902682  0.511195309 -1.6306665455
## 392  -0.892470664  1.208164452 -0.0394208892 -1.125790974 -0.4913664468
## 393   1.263532385  1.214499540  0.2415021073  0.076183845 -0.9748779086
## 394  -0.775586874  2.032783646  0.0620480697 -0.921826190  0.2848009142
## 395  -0.012932602 -0.764001164 -0.5009974970  1.143425071 -0.3790070394
## 396  -0.687958522  1.250448325 -0.6560700676  0.662185994  1.2927329055
## 397  -0.220809834  0.955100619  0.0232169893 -0.274109035  0.0798930460
## 398  -0.571018403 -1.262073170 -0.5782321357 -1.037277777 -0.6547819782
## 399   0.323721812  0.491070589  0.2016440553  1.727756099 -1.1218542989
## 400  -0.791697614 -0.770206758  1.3300176160 -0.497976448  1.2450754654
## 401   2.562090655 -1.586183904  0.0192263499 -1.164726227 -0.3556311971
## 402   0.720921038  2.698099583  0.2550441827  0.196426185  0.7855741773
## 403  -0.193817811 -0.875640605  0.1137972609  0.193862859 -0.8396113342
## 404   0.567302319 -0.181812118  1.3295417995 -0.457480373 -0.6799979974
## 405  -0.146153562 -1.131006043  1.4343982238  1.229580138  0.3406256544
## 406  -1.263374241  0.609585032  1.4052605471 -0.440558821 -1.4275853129
## 407   0.519217614  0.401591469 -0.0899752785 -0.835515105  1.1342189974
## 408  -0.579959792  0.265731927 -1.6867630967 -0.034727114 -1.2286454181
## 409   1.244440288  0.316074222 -2.6578165257 -0.182873818  1.5044046543
## 410  -0.115141564 -0.330373623  0.0205778350  1.832162340 -1.3320332420
## 411  -0.313891903 -0.470768837 -0.5819444599 -1.199219625  0.0879957294
## 412   3.420317662  1.147593859 -0.6003398712  1.047976812 -1.1454106333
## 413   0.385973512  0.098905438 -0.9272029049  1.313212254  0.2817759715
## 414   0.243996028 -0.514855791  0.4000815983  1.289224030  0.6484875243
## 415  -0.833145724 -1.427659713  0.6908579368 -0.911874008 -1.2530608752
## 416  -0.769502515 -0.892789449 -0.9439288151 -0.001154126  1.2332493122
## 417  -0.738666341 -0.706630654 -0.7088567332 -1.234430280  1.1832003331
## 418   2.459995535 -0.703136272  0.1341712581 -0.735624962 -0.1645687136
## 419  -0.998033910 -0.482490072 -2.3894145281  2.032476666 -1.5590585877
## 420  -0.961328087  0.335858340 -2.4852424969 -0.159170023  0.3374521554
## 421   0.624400951 -0.429881177  0.1641236987 -0.717795340 -1.0260813487
## 422  -1.096140710  1.080555455  1.8115842157  1.377274890 -0.1883886209
## 423  -1.222149411 -1.444076038  0.3864156193 -1.775013818 -1.6370874352
## 424   0.257209964 -0.521160563  1.5234942053  1.935119865 -0.1063533340
## 425   0.833264581  1.139517735 -1.6594638798  1.968615129 -1.3208389955
## 426   3.291976356 -0.697435479  0.1676585967  2.193495945 -1.0035472809
## 427  -0.105756589 -1.107057400 -1.5036311920 -0.549559909  0.0330224205
## 428   1.968909803  0.669844523  2.2406144953  1.885664839  0.3549105311
## 429  -0.094648499  0.605536255 -0.7702152128 -1.450423174 -1.2158525457
## 430   0.671481119  1.807318302 -1.9387647125 -0.277441896 -1.1346784191
## 431  -0.208890517 -0.812051333  0.1024342141  1.319399441  0.9446808958
## 432  -0.464288896  2.289496850 -0.0916666697 -0.429735509  0.3037239235
## 433  -0.433024451  0.258696548  0.0838627797 -0.815583992  0.8393844697
## 434   0.312491597  0.189063609 -0.6849326466 -0.401210231  0.2028394054
## 435   0.890647106 -1.715236387  1.6588708697 -0.499778945  0.4511330792
## 436   0.417884502  0.094769351  0.9660074189 -0.462947819 -0.1203459038
## 437  -0.866172058  0.253468773 -0.6892898054 -0.742835685 -0.9763574831
## 438  -0.711552970 -1.506163640  0.6589691823 -0.191690699  1.3800796679
## 439   0.120205850  0.135012074  0.0913633524  0.522275761  1.1301498097
## 440  -0.367164670  0.138989875  0.1112269239  0.848381319 -1.5309860087
## 441  -0.515906947  1.872259496  1.4033062462  1.515417967 -0.2761342920
## 442  -0.747101048  0.333176453 -0.0791007670 -0.796959766 -0.3685646744
## 443   0.637148350 -0.154909020 -1.4766266088  0.257793880 -0.9437943889
## 444  -1.228563792 -0.515729037  0.0365003886 -1.007039477  0.6665474450
## 445   0.350937617  0.763659787 -0.6305843549 -1.006788512 -1.1462393738
## 446   1.736218260  1.520078605  0.7085896367  1.083234981 -1.8120206611
## 447   0.535990566  0.403071650 -0.6602376310 -0.533244997  1.4479030782
## 448  -0.267386417  1.387160009  0.0331409194 -1.263889472 -0.4193640940
## 449   1.582597432  0.717140455  0.0729233198 -0.646227911 -0.5008143043
## 450   0.028273530 -1.204146174 -0.0473766925 -0.384403360  0.5413917416
## 451  -0.202164147 -0.825115779  0.2725248652 -1.956866342 -0.3425787279
## 452   0.509040504 -0.128986004  0.4482259284  2.538489115  1.1784871309
## 453   0.397190775 -0.574210431  1.5775085312 -1.022297699  0.9286208941
## 454  -0.587861147 -0.617799566 -0.7435519170  1.358466657 -1.0132792392
## 455  -0.680213736 -0.167763454  0.4075965802  0.071314068  0.9917527736
## 456   0.614626402  1.100069719  0.1492477946 -1.055695051 -1.9204195126
## 457  -0.238396507  1.558315909 -1.5293450176 -0.493080413  0.5361957507
## 458  -1.549411703 -0.747788031  0.8091714088 -0.317112316 -0.8161749226
## 459  -0.022532030  0.585345589  1.3847556695  2.270434819  0.3617344511
## 460   0.257911969  0.343326601  0.0424410150 -0.869730179 -1.7961883011
## 461  -1.228077751  0.078488880  0.1157414786  1.687228707 -1.2527803933
## 462  -0.301926730 -0.383523843  0.0317657281 -1.031386115 -1.6552241275
## 463   0.262990067 -0.526148841 -0.4888632025  1.027249825  0.7123790523
## 464  -1.179433169 -0.472468888 -2.3943825199  2.166968153  0.2059557233
## 465   0.056161035  0.139537379  0.3057042480 -1.901180439 -0.7376325943
## 466   0.061868041  0.586823120 -1.0414066144  0.860181747 -0.8412468758
## 467   1.657510048  1.821327359  1.4481408872 -0.402704166 -0.8320484714
## 468   0.438794412 -0.003757226  0.7656404442  0.184342071 -1.8218016082
## 469   0.570949128  0.255538488  1.2068645031 -0.032850637  1.4447840905
## 470  -0.838344166  1.591047919  0.1041606830 -0.088063565  1.0979039145
## 471  -0.925328502 -1.203149207 -0.4788088620  1.259635866  0.8551351666
## 472  -0.133841702  0.353143109  0.0258696775 -0.185778914  0.2568839464
## 473  -0.407284561  1.547397395 -0.2381913997 -0.362165716 -0.6183737983
## 474   3.787325083 -0.662558534  0.1617248881  1.036650724  0.7756849701
## 475  -0.656718550 -1.042495778 -0.4688768780  1.106562899 -0.8718925789
## 476  -0.357999901 -1.207119704  1.7539860209  1.546614299 -1.5092992570
## 477  -1.191906463 -1.046523028  0.7653792314  0.920928852  1.1940923711
## 478   3.655150280 -0.797572457  0.7220171887 -0.426030390 -1.6199374772
## 479  -0.654668419 -1.659164159  0.0702965529  0.146791073 -0.4117417494
## 480  -0.734949689 -0.855457126  0.1375744323 -0.354558531 -1.7234033395
## 481  -1.044033292 -0.068316946  2.3853977350  0.299191597 -1.0076160850
## 482  -0.298145957 -0.978269890 -0.6564508157 -1.349652838 -0.6143531739
## 483  -0.916265633  0.640671623 -0.4462389063  1.831637528 -0.7084579552
## 484  -0.662532829 -0.079178857 -0.6110781315  1.051268692 -1.3087099709
## 485  -0.254140599  0.253629164  0.4087869102 -1.268024283 -1.8723226477
## 486  -0.816349902 -0.433166407 -0.7968780471  0.147437254 -1.8862225694
## 487  -0.149143185  0.640288556 -0.9315502758 -0.549759292  1.2437084190
## 488  -1.209037365 -0.929527018  1.7344353515 -1.192745435  0.8641423944
## 489   0.336269942 -0.155937180 -0.6158063392 -1.021301464 -0.1394195937
## 490   0.551178490  1.317441223 -1.5776683813 -0.429266660 -0.6973316677
## 491  -1.077038413 -0.001810204  0.2649310984 -0.240962345  0.8213791078
## 492   0.214092355  0.910293833  0.0865202418 -0.002708221  0.6841285200
## 493   0.395152472  2.594804146 -0.6077577703  0.288231524  1.4117883900
## 494  -0.276017939  1.057464414  0.9276695148 -1.592480837 -1.7391753253
## 495  -0.238933466 -0.672615601  0.0902603599  0.446880789  0.0834161853
## 496  -0.787684397 -1.503977237  1.3280143033 -0.464170358  0.5149296713
## 497  -0.948368238 -1.683463404  0.1170985978  1.085485976  0.4746264855
## 498   1.121642569  0.949068378  0.3086487194 -1.701686961  0.9019948687
## 499  -1.073247539 -1.750940550  0.0542254063 -0.632009175 -1.3339109271
## 500  -0.046181445 -0.416233036  0.1202627847 -0.132514690 -0.1614107643
## 501  -0.190979847 -0.118874892 -1.4741668013  0.128168601 -1.8373810494
## 502  -1.016374551 -0.488135834  0.0559925578 -0.785031142  0.0851377809
## 503   1.039766997  0.656666025  2.0988906299 -1.286046657  1.7628628272
## 504  -0.144797362  0.114179437 -1.4645540495 -0.553809258 -1.2005992826
## 505  -0.491099368  0.900518716  1.3666249006  2.193069109 -1.6532575815
## 506  -0.866394312 -0.825422174 -0.5506968797 -0.718834700  0.0189314467
## 507   0.655971813 -0.564388030  0.0553705360 -0.771098755  0.1041645815
## 508  -0.382903990 -0.884073244 -0.8944857651 -0.387803418 -0.5139923505
## 509   0.940179273 -0.665373276 -0.5131080665 -0.565897833 -1.0794940633
## 510   0.403806200 -0.121684111 -2.4497451123  0.222994114  0.2872870520
## 511   1.214890578  0.619587961  1.6114913440  0.736720371  0.0092914407
## 512  -0.121962876 -0.298496588  0.6639123293 -0.062905965 -0.4408559923
## 513  -0.799484065 -0.647929534 -0.5228347837 -0.941039161 -2.0046749058
## 514  -1.384362393 -1.650336128  0.0738581308 -0.173733928  1.3399784056
## 515  -0.176387214 -0.480234586  1.3871335240 -0.214888777 -1.6175772702
## 516  -0.938870366 -0.314252667  0.0147364080 -0.782735841  0.1105279456
## 517  -1.103785340 -0.452949168  2.3808445851 -0.685282304 -1.6743643704
## 518  -0.697004863 -0.936260366  0.7874738116  0.079520552  0.9280951121
## 519   0.042626237 -0.479318916 -0.5774247581 -0.450750241  0.6861072724
## 520  -0.215745032 -0.597241061 -0.5201305547 -1.125819190 -1.0954325310
## 521   0.028604057  0.080296475  0.4971256745 -0.951264471 -0.1127096153
## 522  -0.369999407 -1.666045693 -0.6318227055 -1.184819159  1.3229802223
## 523  -0.587519982 -0.228687450 -0.6752331281 -0.480386665  1.2900646879
## 524   1.376708008 -1.419366109 -0.0199747408  1.878147685  1.4361770315
## 525   0.377174474 -0.704594620  1.6918813704 -0.334743647  0.9330707163
## 526  -1.381722182  1.033058762  0.0459171145 -1.229227950 -1.0988434360
## 527   1.097924701 -0.618287410  0.1100448109 -0.639726065  0.7130734666
## 528   0.117450438 -0.771376227 -1.4943944065  0.253148656  0.9907867435
## 529   0.181655226  0.304768621 -0.1107673735 -0.465954662 -0.3645753400
## 530   0.431853092 -0.288616281 -1.5273101214 -0.656944299 -0.9905455070
## 531  -0.017912433 -1.054011993  1.3936164642 -0.513139028  0.3369416269
## 532   0.348798179 -0.560158769 -0.6188115827 -1.244742141  0.3703036160
## 533   0.168964025  0.655601738  1.3423472738  1.018927719  0.9562823794
## 534   1.207115621  0.776537002  1.4189886293  0.000795877  1.0198181898
## 535   1.135297417  0.769480048 -0.0740082128 -0.525285422  0.3351001873
## 536   2.470295948  0.140752454 -1.4551061654  0.199300468 -0.8430273099
## 537  -0.210697556  2.983211719  1.2046478674  0.878796879 -1.2877003437
## 538   0.074787648 -0.942580118  0.4802489679  0.946516605  1.3086877765
## 539   2.731197789 -0.886429583  0.0910285899 -0.940657186  0.9761847434
## 540  -0.521954017  2.172618026  0.6028135721 -0.125910484  1.1931774690
## 541  -0.996739770  0.539305991  0.6879380880 -1.032797435 -1.1684652868
## 542   0.086347323  1.823801888  1.3644254337 -0.079998432 -1.1730905044
## 543  -0.323081012  0.460940659  0.9356660528 -1.658570186  0.2098300421
## 544  -0.149943191  0.119676494  0.0279346249  1.390696662 -1.5427456237
## 545   1.854888578  1.506533352 -0.9324577149 -0.507063316  1.4635302814
## 546  -0.472350061  1.509064567 -1.3711230000  1.978421925 -0.0165237992
## 547  -0.980502511 -0.541109985  0.0873031892 -0.040439612  0.0866418922
## 548  -0.762696418  1.146549948  0.0022112608  0.725396293  0.4037681789
## 549  -0.112014098  0.314979998 -0.6569552106  0.127913231  1.1139861258
## 550  -0.290760168 -0.318904493  0.0184252992 -0.437232533 -0.4610283669
## 551  -0.952163488 -1.543787076  2.3224283732 -0.255312394 -0.4159567501
## 552  -0.407571407  2.059618080 -1.2343095193  0.174000720  0.7055517425
## 553   1.029567276  1.719769206 -1.6938962052 -0.174982083  0.5549519932
## 554  -0.374358063 -1.222652778 -1.6939295140 -0.775060069  1.4311827942
## 555  -0.781508194  1.472743031 -0.4687040690  0.930251293  1.5156426197
## 556  -0.956877701 -0.517345499  0.7492229643  0.263532290  0.9970551511
## 557  -0.178095662  0.411331148 -0.7709538571 -0.768073376  1.1007000749
## 558  -0.638677852  0.354919315  2.3194875242 -0.797435752  0.8273129480
## 559   0.149820435 -0.505193097 -0.4660426752  1.288246214 -1.9310617400
## 560  -1.116268080  2.128295503 -1.8326180992  0.072804880  0.9864021174
## 561  -0.915024089  1.201209103  1.4326075616  0.332043902 -1.0097008149
## 562   3.815425443 -0.579163100  2.3576196249 -0.486459705 -0.1259971196
## 563  -0.133895713 -0.359384445 -1.4959196766 -0.599480679  0.7654703781
## 564  -0.334285654 -1.599746496 -1.4863112402  1.730949565  0.5383406062
## 565   0.512186577 -0.802335586 -0.0642787273 -0.949524251 -0.5623012142
## 566  -1.023825839 -1.463740467  0.0575218939 -0.249971457 -1.2745204860
## 567   0.111550050  0.351145900 -0.0265711762  1.541876172 -0.3246899837
## 568  -0.012138992 -0.659919942 -0.6049580070 -1.136034997  0.9358259949
## 569   1.479869010  1.582890949  1.2152957972 -0.617668916  1.4101551155
## 570   0.325231991  0.014255444  1.4294942746  0.369262206 -1.7987819251
## 571   0.268111824  0.118115164 -0.6622785870  0.790644699  0.7888202966
## 572  -0.944866037 -0.540214821 -0.6157202354 -1.482886155 -1.4185892874
## 573  -0.470392971  0.090989510 -0.7810133707  2.178521034 -0.5796120938
## 574  -1.010952484  0.872675470  0.4781950409  0.612011975  1.3414357394
## 575  -0.569075168  0.100969203 -0.5871150149 -1.228017294 -0.9880917042
## 576  -0.135933075  2.786116392  1.2738588091  1.254570431  1.3495422424
## 577  -0.516232023 -1.821808856 -0.6229093354 -0.647847496  0.4089455069
## 578  -0.461625527 -1.084717917  0.3331592571  0.902545424  1.5317232210
## 579   0.345174547  1.167493687  1.3970364292 -0.408090666 -1.5795199683
## 580  -0.352946319  0.038633369  1.4037309924 -0.238738425 -0.0490806035
## 581  -0.710144438  0.091665505 -1.5221139787  0.022782126 -1.8188247318
## 582  -0.868932416 -0.030004910  0.0524037418 -1.061048625  1.0593624742
## 583   0.043428642 -0.673687622  0.6252579088 -0.671683103  0.3668592917
## 584  -0.614189026  0.457006935  1.3204891855  0.027833285  0.6012911467
## 585   2.804344273 -0.835553520 -1.4927664095  0.007216997 -0.7372569062
## 586  -1.446846370 -0.503843988  1.4306489445  0.079696603  0.1280404142
## 587  -1.176862265 -0.614494372  0.7813384834  0.128054572  0.0963210467
## 588  -0.286790083  2.256460199 -0.0529535006 -0.083628159  1.1999048255
## 589   1.101840791  1.256394732 -0.0703920901 -1.167139006  0.4253003065
## 590  -1.131100097 -0.645161654  1.3316045324 -0.565460056 -0.5074979495
## 591   1.140748643 -1.251463306  1.0662605048 -0.781411194 -0.0532729581
## 592  -0.784634730  0.825299747  1.3903956605  0.940475084 -1.3736995275
## 593   2.978135111 -1.138978827 -1.5864787571 -0.673643931  0.3645887041
## 594   0.149084421 -0.738257097  0.7040809937 -0.647862397  0.0782254746
## 595  -0.191282626 -1.333736830  0.1262138347  1.342907293  0.2683232587
## 596   3.610860764  1.357739604  0.6784186615 -0.639929994  1.1418171925
## 597  -0.847564075  0.509223300  0.0508550038 -0.966590720  0.8676782274
## 598  -0.421153662  1.407586833 -0.7459400487 -1.662937559  1.5915716236
## 599  -1.151932073  1.238149051 -0.8423829046 -0.517141545  0.1847601443
## 600  -0.694170534  0.403636893  0.7058351796  0.470241102  0.2905091367
## 601   0.525352726 -0.943153341  0.1079048068 -0.596018488  0.0470056802
## 602  -0.732590410  1.581676482  0.0486277289  0.424378246 -1.5690091309
## 603  -0.908779015  0.684278308 -1.5565949067 -0.878566638  0.3424168191
## 604  -0.555462475  0.090433741 -0.0660254491 -0.927402922 -0.7092525034
## 605   0.159385576 -0.159114569 -0.2059696022  2.776295371 -0.6169395586
## 606  -0.359603130  0.371112511  0.4081776762  1.113614927 -1.4134267914
## 607  -0.449392448 -0.284621866 -0.5330144081  0.450027677 -0.1541967291
## 608   0.907090526 -0.393016179  0.2658866134 -0.680427124  0.0559012349
## 609   0.522119489  0.190440087 -1.7980007757 -0.941508742  0.8153539256
## 610   0.701002866  1.093198443  1.2922939468  0.521928797 -0.1441752267
## 611   0.647426223 -1.703907453 -0.5954813877 -1.032720530  0.4579846792
## 612   0.466324500 -0.203912498  1.0165775657 -0.932052516  0.1227398815
## 613  -0.305518698 -0.328817721  0.8021320440 -0.510601590 -1.0074629323
## 614  -0.606437060 -0.822615944 -2.5502503663 -0.127997617  0.3965360369
## 615  -0.517190193 -1.304277688  0.0835888315 -0.594233787  0.2465572679
## 616  -1.239890742 -0.531283693 -1.5279498707 -0.550703845  0.9942645290
## 617   2.449856926  0.352817630 -0.8340150332  2.205155133 -1.6675456831
## 618  -0.453377441  2.164812159 -0.3379098616 -0.214779504  1.5431878644
## 619  -1.336777539  0.461710168  0.3756445001 -0.288511216 -0.8300557518
## 620  -0.197940899 -0.426216795  1.3780424096 -0.443569224 -1.6120189487
## 621  -0.505987857 -0.960842553  0.4027022216  2.673608004  0.6981069140
## 622   0.939905536 -1.236692104 -1.5610233148 -0.775635332 -0.5708530436
## 623  -0.491546878  0.120726025 -1.4722836395  0.544807760 -0.9090940588
## 624  -1.042917747  1.872392567 -1.5049134910 -0.573511705 -0.5894882017
## 625   0.542841691  1.366575740 -0.7950182902 -1.047497913 -1.0628370308
## 626   0.373284531  0.874552644  1.2994891427  0.254406786  1.2818832064
## 627  -0.619438892  0.245444807 -0.9190300954  0.004462048  0.5820049353
## 628   1.418023609  0.766714507 -0.6108981772  1.260981243  0.0669028853
## 629  -0.533990130  0.865350555  0.0836619207  0.555579935  0.9557981732
## 630  -0.427960326 -1.162787305 -0.5882604308 -0.616043600 -0.6335303054
## 631  -1.300706792  0.314514186 -2.4815605136 -0.559970071  1.5047391920
## 632  -0.468015443  0.675290496 -1.5957444505 -0.025839907 -1.7192788280
## 633  -0.720298132  0.130720786 -0.7892368631 -1.519010864 -0.1439129177
## 634  -0.530044828 -0.439338504  1.3587966060  0.318641839 -1.6243587469
## 635  -0.712512740 -1.355162984  1.3506985536 -0.394663419  0.5517605611
## 636   1.329267201 -0.978029686  0.1236514812 -0.054185635  0.9456671027
## 637  -0.180760595 -0.158892046 -0.1219283119  2.513059834  0.8691732082
## 638  -0.646604883 -0.888732722 -0.6107857763 -1.196641339  0.8773251346
## 639  -0.630092772 -1.520021836  2.2997402674 -0.776698983  0.4703690666
## 640  -0.189258503  0.549356265  1.2278275680 -0.496735033  0.3050121435
## 641  -0.756449962 -1.738888134 -1.5575688397 -0.606611066 -1.2934571350
## 642   0.169671504 -1.004710003  0.7107105513 -0.365390389 -0.5561561465
## 643  -0.600861045 -0.375304949  0.6777847323  0.141039435 -0.7561362960
## 644  -0.098720811  0.113931672 -1.6211794331 -0.607291742  0.2354579262
## 645  -0.586427016  0.059770366 -0.5267088000 -0.127758100  0.7947217934
## 646  -1.128288024  0.724869348  0.0514010898 -1.199376534 -0.5654511323
## 647   0.492094263  1.352348227 -0.7556258627 -0.810432628 -1.3568230476
## 648   0.882391272 -0.235421122  0.8091521669  1.812499114  1.1129936325
## 649  -0.531470468  0.103737606 -0.6340450277  0.648511024  0.4921602082
## 650   1.580201376  1.423286653 -0.6198016072  0.974547390  1.0812382279
## 651  -0.139870893  0.639943219 -1.6400670030 -0.881384210  1.2155776596
## 652   0.353140255 -0.840880617 -0.7457603806 -1.193654755  0.2869252680
## 653   0.439179226 -0.824573200  0.7172422461  1.097014854 -1.3921405192
## 654   3.492044924 -0.281415174  1.4124333900 -0.180530546 -1.7938736750
## 655  -0.457088841  1.358907883 -0.6727381721 -1.410740414  1.3041289734
## 656  -0.718804864 -0.453794480  1.6026362004 -1.123451822  1.2342149115
## 657  -0.991163434  0.181488322 -2.3983441855  2.311356355 -1.7299446909
## 658  -1.020016238 -0.145860766 -0.6660422744 -1.014098576 -1.0522329034
## 659  -0.044519031 -0.426498919  1.2689282794  0.338122572 -0.4507880654
## 660  -0.549977563 -0.338417608 -0.5211775578 -0.790684696 -1.9399540310
## 661  -0.597719971  1.873520359 -1.8766700911 -1.165907896  1.9823097359
## 662  -0.533327482  0.767462465  1.5675217701 -0.658408115 -1.4849019693
## 663  -1.321367473 -0.725793305 -0.8097495953 -0.385256904  0.1058105447
## 664  -1.206664794 -1.566654017 -1.5083152263  0.883584570  1.4011523652
## 665   0.917040627 -1.848991606 -1.5644916637  0.564259644  0.4950668107
## 666  -0.227796547  0.445094675 -1.6318865567 -0.573619304  0.8805058690
## 667  -0.768737670 -1.970268193  0.9986169480 -1.423228738 -0.5407548829
## 668  -0.340864056  0.895818704 -1.5794430420 -0.684611753 -0.7851930698
## 669  -1.190979756  0.412228660  0.0833433172 -0.289546415  0.2682451181
## 670  -1.194266366  1.829910030 -0.5946293704  0.842838235  1.5437314948
## 671  -1.102696788 -0.563286533  0.0825658154 -0.698014674 -0.8082752667
## 672  -0.950297433 -0.228674253  0.7032123800  0.211283082 -0.7273379167
## 673  -0.240802471  0.948598378 -0.0370897692  0.062512123  0.6604003337
## 674  -0.906124211  0.637214099  1.3859651949 -0.435942231  0.0508992125
## 675   0.975499830  0.725783826  0.5357386977 -0.388728455  0.3328210344
## 676  -0.519821628  0.038065067  1.0665548167 -0.804279085 -1.0136575743
## 677   0.035804530 -1.283680291 -2.5137447875  1.751019539  1.5245826622
## 678   1.852981270 -0.108638239 -0.2995661696  0.430291460 -1.1842818318
## 679  -0.735247854  1.423141108 -0.9495301168  1.486991939  1.0944719178
## 680   0.129474918 -1.049470594 -0.8389602083  1.484865598  1.2561851343
## 681  -0.194919990  0.080026070 -0.5722706280 -0.581862857 -0.9775899189
## 682   1.426024045 -0.531917523  1.3876531669 -0.411747230  1.0518850758
## 683  -1.107578427  0.898392437  0.6850840942 -0.906109930  0.3662067353
## 684  -1.148074594 -0.980321285  0.7636431572  1.110890692  0.3239736264
## 685  -0.186552419  0.869485466 -0.2359764210  0.658488238 -1.6318230960
## 686  -0.520331904 -0.659036133  1.4269593249 -0.416524272  0.1156644727
## 687   0.872347495 -0.376973526  1.3699924377  0.183063125  1.0778250274
## 688  -0.137586689  0.449849732  0.0807090694 -0.838121689  0.0006023485
## 689  -1.270457645 -1.031651051  1.8041298971  0.952390518  0.8714002691
## 690  -1.364540689 -0.569834801  1.4536893411 -0.175055223 -1.6469979233
## 691   0.035034174 -0.862703787 -2.4260623506  0.981956565  1.0269743499
## 692  -0.995908325  2.108077938  0.6770223950 -0.055660900  1.1904495483
## 693   0.053466913 -0.266225064  2.3821444407 -0.619964857 -0.1440481676
## 694   1.269515020 -1.691660819 -0.6484618220 -1.170139087  0.4648141452
## 695  -0.041283607 -0.834618215 -0.6015320042 -1.259369849 -0.8682037806
## 696   0.671847671  1.072988060 -1.7958831225 -0.089371600 -1.5263333212
## 697   0.229950200 -0.378611288 -0.3489088505  0.033526278  0.4744806656
## 698  -0.795402121 -0.763722847 -0.5311351527  0.779498326  0.0447022454
## 699  -0.258139672 -0.505243066  0.0866768244  0.829461157  0.1131138102
## 700   1.700149826 -0.003768242 -1.7032957158 -0.960276943  1.4020922866
## 701  -0.275593590  1.265075493 -0.1759127953 -1.015246958  1.2656582901
## 702   2.037158115  0.514182225  0.8570940911 -1.643176081  0.5514052547
## 703  -0.081029260 -0.263319687  1.0056616534 -0.960888651  0.3982529223
## 704  -0.033633649 -0.468039149 -0.6176186461 -0.308839838  0.0890196074
## 705   0.202528072  0.872186083 -0.5637877381 -1.111876259  0.9544060697
## 706   0.410615340  0.133312599  0.1076465042 -0.711964647 -2.1161615032
## 707   0.079742506  0.965684284 -0.2301704107  1.981661735 -0.4196461697
## 708   1.393098289 -0.454356378  1.0330156733  0.327575571 -0.1855594164
## 709  -0.207174751  0.586951899 -0.5709401307 -0.567001950 -1.7617173090
## 710  -0.809537820 -0.974659100  1.3536092402  0.365396007  0.3297636177
## 711   1.343522737 -0.723887639  0.1497876278  0.682683376  0.9962703146
## 712  -1.454318799  0.960826907  1.3830428687  0.322916115  1.2874357995
## 713  -0.685742701 -0.777710988 -0.6707759089 -0.256583537 -0.2846035952
## 714  -0.265411431  0.636140990 -0.6734243062 -1.217638751  0.8700373025
## 715   0.919285599  1.901602067 -1.7255906231 -1.267509788  1.7502227805
## 716  -0.234566137 -0.089075948  0.7532991831 -0.625460371 -0.0901112228
## 717   2.394694531 -0.540426425  1.0400169156 -0.712375501 -1.6659459924
## 718  -1.454263896  1.861853482  0.8004671206  0.660893044  0.2858605966
## 719   0.235554804 -0.535662117  1.3136451247  1.875264855  1.3202897313
## 720   0.447654372 -0.711529416 -0.7339900568 -0.976545773  1.2040806492
## 721  -0.854377835  0.125250627  0.1225006270  1.125277873 -1.5307961462
## 722   1.598415701  0.270521058  0.0324135434  1.386085903  1.1726208241
## 723  -0.618943360 -1.093645888 -1.0037816114  0.311821411  0.5969641446
## 724   0.637741688  0.728964921 -0.0639983474 -0.641554221  1.5074005982
## 725  -0.674473021 -1.629995337  0.0846918615  0.570136031  1.3638922876
## 726  -0.631792109  0.340174346 -1.1251687841  1.735957102  0.0997320150
## 727  -0.619306597 -1.090751945  1.2926013919 -0.622495067  0.5885175369
## 728  -1.532191432 -1.329803727 -0.5487192168 -0.940780683 -0.6799151628
## 729   0.918548848  1.819366167 -0.0533108756  0.429535548  0.5529594377
## 730   1.148765128 -0.420400456 -0.7362553121  2.205439581 -0.0494941781
## 731   0.353495729 -0.955397867  0.4532104942  0.696404741 -0.4674689198
## 732  -1.332511610 -0.696183179  1.4774665965  0.638208469  0.9915421679
## 733  -0.817141545 -0.697499170  0.7315121142 -0.266453982 -0.8103041644
## 734  -0.162349646 -1.408771715 -0.5758645429 -1.191835491  1.0941718384
## 735  -1.138782873 -1.252530716  0.4355765626  0.615928274 -0.2577687230
## 736  -0.260767078  0.450430681 -0.0723372016 -0.568977549 -1.5177170431
## 737   1.205296094  1.542890886  0.0187784397 -0.785438915  0.2222851273
## 738  -0.577492935  0.760624241 -0.0630264206 -0.642659291  1.4898278795
## 739   2.026085500 -1.806751351 -0.6509931742 -1.340887502  1.3416891030
## 740  -0.676314667 -0.585564461 -0.5254657257 -1.075317656 -1.9935633597
## 741  -0.553620622 -0.307585863 -1.5528699554  0.158156456 -0.7194560234
## 742   0.712860231  0.784476082  0.8935237903 -1.466331224  1.4591406184
## 743  -0.527852031  0.954176824 -0.7507897799 -0.592111009 -1.4467764945
## 744   1.252043097  0.889168746 -0.7972370838 -1.327461012  0.3231420908
## 745  -0.988480412  0.917758543 -1.2567284194  1.006469214 -1.0053024777
## 746   0.611346335  1.088289181  0.6377535014  1.106043655  0.1358105202
## 747   2.709368907 -1.526472127  0.0241539006 -0.531521247 -0.3374076152
## 748  -0.704491486  1.940825107 -0.6358577361 -1.306552678 -0.6476236810
## 749  -1.246603076  0.943688212  1.4324745489  2.147466962 -0.1605044830
## 750   3.974571592 -1.655058990 -0.6902523148 -1.266859880 -1.2499199820
## 751   1.403648364 -0.065769887 -0.5665670622  1.553102498  1.1017573251
## 752   1.504523142 -0.747291727 -0.0223584880 -0.838737794  0.9562963030
## 753   0.499065919 -0.414006232  1.4756864345  1.369888345 -0.0860110021
## 754   1.740210614 -0.836412360  1.4659772352  1.909667253  1.0355448494
## 755  -0.782618317 -1.339274794 -1.6297924744 -0.186713389 -0.3499969446
## 756   1.646031117 -0.348740488  0.2732672977 -0.905022194  1.2560034172
## 757  -0.593819372  1.618205138  0.1736898213  1.839813134  1.1383229484
## 758   1.011486418 -0.672794639 -1.4654532995 -0.616516569 -1.0353323255
## 759   0.998089472  0.824953470 -2.7332936861 -0.541512841 -0.1863892517
## 760  -0.155826107  0.281990999  0.7233012872  1.830080242 -0.8943530319
## 761   1.279182948  0.147530097  0.5975023463 -0.597948899  0.2491200701
## 762  -1.010444319  1.489437173 -0.9132192552  0.685254923 -1.2468224838
## 763  -1.400035145  0.848513589  1.3909877077 -0.561203710 -1.3855821627
## 764  -0.872555018  0.005016955  0.0877496399  0.046434590 -0.1021353038
## 765  -1.178694855 -1.258831323  0.6683733474  0.090242901  1.4230985745
## 766  -0.739266015  0.647644802  0.0333876487 -0.778642007  0.0088391800
## 767   1.667851051  0.890251030 -0.9461727902 -0.472811470 -0.7454403829
## 768  -0.575454274  0.398095409 -0.2755276472 -0.077705866  1.2117744337
## 769   0.276627054 -0.037321243  0.4589163993  2.697964234  0.3084296554
## 770  -0.840563149 -1.467952633  0.0148269126 -1.175047897 -1.2839487954
## 771   0.820768187  2.479079428 -0.6744405690 -1.622784791  1.2364621405
## 772   0.913548224  1.761001870 -0.0581769087 -1.017842272  0.2340676662
## 773   0.118555474  0.591335247 -0.1160553467 -0.217199619 -1.4894478262
## 774   0.957759153 -0.296909976 -1.4100999482  0.684868449  0.5271634508
## 775   1.467979139  1.037053403  2.0825576313 -1.317071112  0.9478630132
## 776   0.069115610  0.907387844 -0.6277310796  1.056720602  0.3579365457
## 777  -1.143467998 -1.044472197 -0.4980124660 -0.378468270  0.8695700881
## 778  -1.509582445 -0.469788203  0.5172473670  1.008178673  0.1967773371
## 779   0.492826233  1.797424964  1.3503612645  0.231383002  1.1917950040
## 780  -0.017160421  2.220688310  0.8928336563 -1.368735717 -1.5058679618
## 781   0.172691045 -0.924112841  0.5192162533  2.410924059 -0.4364943933
## 782  -0.750540071 -0.877391660  1.3751889266 -0.560773266 -1.4166076669
## 783   0.081489214 -0.582270521  0.5211434892  2.081770409  0.2094104779
## 784   0.195119513 -0.813962457 -0.0185720402 -0.404568024 -0.5526498258
## 785   1.404259062 -1.793953911 -0.8954295239  1.163142997  0.5393674349
## 786   0.775234154  0.563718883 -0.5358566313  0.704801595 -1.7328534582
## 787  -0.737415588  0.129521614  0.1897866496 -0.116555747 -2.1164892592
## 788   0.637753435  0.243185394  0.4540242491 -0.931146847  1.6870484567
## 789  -0.371597660 -0.515022957  1.0669022389 -0.550138458  0.0647838465
## 790   1.230406393  1.207833994  1.2875648565 -0.783364848 -0.1023855733
## 791  -0.384584564  0.202782348 -0.6077928643 -0.964519761  1.0950476779
## 792   0.429707735 -0.638376716  1.3852183549 -0.079804819  1.0101316142
## 793   0.319337664 -0.515380567  0.2105567359  2.127298340 -1.9005982963
## 794  -0.897451636 -0.862558369 -0.8653104052  0.885398939 -1.3896963557
## 795   0.073300472 -1.383539498 -1.6253127362 -0.751790484 -1.2283848122
## 796  -0.347647761  0.267603588 -0.5859689808 -0.283142019  0.8173418232
## 797  -0.362975012 -1.953361536  0.3350426904 -1.547473149  1.2222722582
## 798  -1.188499507 -0.454021858 -0.8020819233  1.587742989 -1.5966007732
## 799  -1.035121100  0.456804045  0.7534957713  1.686019956 -1.4583471810
## 800   2.592639574 -1.285819475  1.3603718480 -0.328191378  1.2210834871
## 801  -1.114300739 -0.378794954  0.7225700705 -0.771133018 -1.6439708070
## 802  -0.339673691  1.151547961 -0.0712559826 -1.016648133  0.9684346252
## 803  -0.504650433 -0.649416848  0.7199139478 -0.029872369  0.9703203871
## 804  -0.969692404  0.487065946 -0.6008204252 -1.066005083 -0.0415424566
## 805   1.155255874  0.862358945 -1.6099574526 -0.877487633 -1.6667411199
## 806   0.940989480 -0.133929271  0.0641560921  0.008070346 -0.9767159611
## 807   0.632181921  2.109723205  0.6223581449 -0.276328533 -0.5607395239
## 808   0.519400619 -0.357927193  0.1035371796  0.090419160 -0.1412541292
## 809  -0.594340000  0.186550057 -0.4563258721  1.640111783 -0.0376706613
## 810   0.081845676 -0.885610433 -0.1659802374  0.061717665  1.0032836673
## 811   1.726731291 -0.419574234 -0.0789880024 -1.122082085 -1.0581009798
## 812  -0.642778017  1.089329410  0.6002337148 -0.970503009  1.5683153895
## 813   0.348108145  1.685414489  1.3720850051  2.032395634  0.5854591123
## 814   1.301696989  0.701438496 -0.6011614158 -1.374206834 -1.4195293684
## 815   2.655814488 -1.001347747  1.0774667230 -0.080738604  0.0310675781
## 816  -1.155966225 -1.680759132  1.6473920939 -1.353657171  1.2931912183
## 817  -0.535086029  2.010208367 -0.2815130976  0.296513762  0.6435901466
## 818   0.522821996 -0.109107386 -0.5100212112  0.593015865 -1.8617424960
## 819  -0.697724429 -0.901948683 -0.5467110698  0.801929682  0.0143689703
## 820  -0.798142224 -1.219863780 -1.2259444224  0.206960175 -1.1136537722
## 821  -0.166987828 -0.987828439 -0.6323545183 -0.260603408  1.1642885604
## 822   0.976466177  1.650449559  0.6640967620 -0.100335539  1.1348455603
## 823  -0.650506337 -0.395019777 -0.9548111856 -0.511010138  1.3275952912
## 824  -0.458933608 -0.818717096 -0.1698637640  0.827631071  1.0098803992
## 825  -0.537630592  0.585840599 -0.6192582001  1.557956668 -0.5921517908
## 826  -0.035891874 -1.546413413 -1.5611307958 -0.171864257 -0.3541150015
## 827  -0.123874732 -0.606759420  0.9595251312 -1.446258485  0.0193062378
## 828  -0.845706600 -0.649905830  0.0912061869 -0.449555909  0.0684951984
## 829  -1.466058157 -1.632657038  0.0802100698 -0.422952917  0.4568664030
## 830  -0.063884885 -0.136185263  1.4394905569  0.466683311 -1.8368749442
## 831  -0.500262385  0.716771567 -0.6201795823 -0.136460025 -0.8728381822
## 832  -0.903326387 -0.364924222 -0.8541828481  0.990133091  0.1790007634
## 833  -0.294404802  0.585439801 -0.6172059192  0.984942105  0.5960216769
## 834  -0.790398382 -0.763943187  0.1038213292 -0.417633306  0.9356607247
## 835  -0.196778519 -1.090459565 -0.9554893623  0.160203779 -0.2656021604
## 836  -0.458753962  0.216917503 -1.7962305733  0.827282249  0.0539549671
## 837   0.120364878 -1.213571966 -0.4756214289  2.765651863  1.6130565031
## 838   1.247420347  1.842588955 -0.8365988453  0.153155820 -0.5241881757
## 839   2.055429180 -0.737506641  0.4734943720  1.320207050  0.2097817619
## 840  -0.326020894  1.744786551  2.2749578345 -0.779060867 -0.6703293991
## 841  -0.546229951  1.024410644  0.0666619010 -1.025812768  0.9829709914
## 842  -1.206017452  0.988988588  0.8228234531  1.501841425  1.3130621801
## 843  -1.037278364 -1.263723495 -1.5838091924  0.216820548  0.5570436333
## 844  -0.327394573 -0.578861563 -0.4957044115 -0.962327818 -1.9736625041
## 845   0.180063599 -0.859390486  0.1265380069  0.007420077  0.0611393632
## 846  -0.656754237  0.187489625 -2.5410751911  2.186003178  0.6046846484
## 847   0.392057022 -0.300215118  1.6572739409 -1.166129614  0.1138026708
## 848   0.406082026 -0.911079304  1.3956284490 -0.318732558  0.9643501199
## 849  -0.616479059 -0.281860085  0.3543981603 -1.327418857  0.6521163933
## 850  -0.564850422  1.893198920 -0.9766617189  0.021938700 -1.1767327257
## 851  -0.964003690 -0.939761636  1.2721417967 -0.532639986  0.6052045593
## 852   1.575641896  1.725054627  1.2578798871 -0.279073628  1.1537287439
## 853  -0.149237566 -1.717317832 -0.6259756656 -0.857988095 -0.4441613406
## 854  -1.383979762 -1.061738388  1.4372499004  0.317324183  0.3215224270
## 855  -0.437688481  0.976316394 -0.9926054902 -0.041075782 -1.3586575088
## 856   0.692530473 -0.726651273 -1.5429327016 -0.686203377  0.9959597367
## 857  -1.261176380 -0.653108616 -0.8060131857 -0.327796382 -1.6465461774
## 858  -0.077168641  0.156977536  0.0317159715  0.076988303 -0.0682021243
## 859   1.689508683  0.309553004 -0.0971612312 -0.606080674  1.4310945964
## 860  -0.658350812 -1.633929111 -1.5635866770  0.593918217 -0.3822068861
## 861  -1.174842102 -0.719153600 -0.4970438907 -0.938543265 -0.2543152213
## 862   2.495523855  1.148163663  1.3598160647 -0.531817871  0.5158316050
## 863  -0.662795529  0.241325087 -0.0163171228  0.670531477  1.1061336723
## 864  -0.464014870 -0.502243167  0.0487602935 -0.891570467 -0.7915519540
## 865  -1.236109513  1.420542941 -0.6587102458  0.616647724 -0.9093982305
## 866  -1.031210796  1.700383746  1.4900829218  2.365353606  0.2967750782
## 867  -0.884170108  1.472336844  0.6598046626 -0.744461717 -0.7092514029
## 868   1.060015146  0.742453174  1.2468326553 -0.507916168  1.2450856194
## 869  -0.601076362 -0.272058695  1.5031777285  1.614604828  0.8045744889
## 870   1.119852579  0.783696770  0.6231127766  0.418422971  1.5491747167
## 871   0.110555290  0.536891090  1.4515556355  1.257540379  0.0745741784
## 872  -1.333160415 -0.721294813 -1.1259105134  1.897091300  1.3590550754
## 873   0.013151181 -0.616053848 -0.8006627972  2.093392361 -0.7130670631
## 874  -0.266470885 -0.163067025  0.0860650587 -0.332868214 -0.1214641492
## 875  -0.201443939 -0.342176423 -0.7946451908  0.288741766 -0.0840888687
## 876   1.347287493 -0.623474707 -0.5015170767  1.971181716  0.7232150406
## 877  -1.104967007 -1.044080975 -0.4600121896  0.880930097  0.0016536529
## 878   0.324198645  0.569895993 -1.6052590485 -0.618318232  0.9218710472
## 879  -0.359909541  2.145932842  2.3050149942 -0.891480644  0.8823666361
## 880   1.133699984  0.219139865 -0.7330657229 -0.485051669 -0.9627423736
## 881  -0.834155792 -0.380959112  0.7352130778  0.557296219  0.1393942972
## 882  -0.244889478 -0.319939753  0.0240230691 -1.037541482  1.3096935184
## 883   0.299096181  0.004130240  1.3580240828 -0.513896683  0.2391517966
## 884   0.310119993 -1.240854136 -0.5477229034 -0.307994022 -1.7974176836
## 885  -0.246578456  1.237690501  1.6107673797 -0.518295114 -0.4895084319
## 886  -0.533706282 -0.787199047 -0.4768418564 -0.174056704 -0.2449372268
## 887  -0.008217437 -1.086309383  0.7571830793 -0.589989691  0.9077946141
## 888   0.203353781  1.487505347  1.4477204383  2.170270434 -1.8084044033
## 889   0.744480309 -0.309426097 -1.5515791477 -0.201960545  0.4899633773
## 890  -0.605418371 -0.533089897  0.5169115609  1.455139049 -1.5591728167
## 891   0.369255541  2.481687153 -1.9726030936 -0.200691429  1.3434166519
## 892   0.180580130 -1.139640740 -0.7603899274 -1.310112881 -1.2450350149
## 893  -1.370801222 -0.898008356  1.7662780532 -0.283203883 -1.7722091514
## 894  -0.714299089 -0.625683385 -0.5894183486 -1.306445690 -1.7208300563
## 895   1.924032593  0.489453363 -0.7234748164 -1.184099394  1.1627982345
## 896  -0.256661044 -0.654373129  0.4338814773  1.018488776  0.4619565146
## 897   0.169348307 -0.657714911  1.4787201117  2.044190926  0.1545595486
## 898   0.401147324  1.293734160 -0.8148449231 -1.216968347  0.3883916362
## 899   1.586802168  0.227895093 -0.6416297294 -1.229540626  0.2391456882
## 900   1.147523185  0.113861874  0.8459297874 -1.490225425 -1.3292548043
## 901   0.039677872 -0.421376279 -0.2332531402  0.046830458  0.1958508159
## 902  -0.749318112  1.059580415 -0.4288546198 -0.373578484  1.5943707246
## 903  -0.761162948 -1.067819681  0.0584244943 -0.771704523 -1.4898331155
## 904  -0.141681367 -0.818335186 -0.5496635572 -0.620551840  0.0346221716
## 905   0.926037891  1.278482183  0.2166432832 -2.082629401  1.2359247363
## 906   0.665117352 -0.126686504 -1.4945753126 -0.900743906  1.1130631815
## 907  -0.828390722 -0.487342783 -0.8632659110  1.551766506  0.1559308822
## 908   2.302289741  0.919889022  0.7152812934 -0.508799608 -0.4346985709
## 909   0.426663961 -0.248108959  0.1881754867  0.215287645  0.4875207166
## 910  -1.199859994 -1.013018493 -0.4438223638  1.277155751 -0.8731805851
## 911  -1.294284732 -1.144056277  0.0629839790 -1.052635863  1.1352410879
## 912  -1.166169760 -1.581073078 -0.5794359226  1.025708901  0.4625170408
## 913  -0.499770484 -1.238248399 -1.5217953176 -0.488400695  0.2915470636
## 914   2.830220620 -0.370437727  0.7224356806 -0.644988882 -1.5593613869
## 915   3.526545544 -1.551646332  0.6131425063  0.038150568  1.4573183936
## 916  -1.324809863 -0.848504735 -1.7792308513  0.823794053 -1.3392256847
## 917   1.833968614 -0.257312391  0.6268062167 -0.575821604  1.3606373806
## 918  -0.524055217 -0.459178000  1.3534882837 -0.316464698  0.1329751461
## 919   3.406672245  0.194169682 -0.2286562039  0.607909295  1.2721036579
## 920   1.070168084  1.916158613 -1.6498812815  0.927391796  1.1958510715
## 921   0.052329371 -0.087510616  1.7170882553  0.660263203  0.1797508335
## 922  -0.827330551 -0.441820886 -0.8225455526 -0.335069688  0.7547741146
## 923   2.903291377 -0.882214752  0.4174573300  0.327579268  0.4767225569
## 924  -0.042086949 -0.020192060  1.6875675906 -0.204506848  0.1786993402
## 925  -0.482124924 -1.388238975 -0.0409420905 -0.599411613  0.4925872506
## 926  -0.975384014  1.729321634  0.6567211472 -0.224798771 -0.6570014029
## 927   1.853751219 -0.229741510  0.3835287657 -1.304976713  0.7265889729
## 928   0.217111669  1.650357059  0.7505761099 -0.738501292  0.2659065211
## 929   0.764195965 -0.394899026 -0.6243126157  0.205279966 -1.6467976342
## 930  -0.762229724 -0.723471645 -0.5799700168 -1.146877883  0.9139741573
## 931   0.183581863 -0.422399732 -1.0573632264 -0.016041681 -0.4506911962
## 932  -0.517541973  0.391872373  0.0512415763 -0.421209224  0.5699387034
## 933  -0.553576023 -0.233283805  0.0979755003 -0.410306784 -0.7238637382
## 934  -1.120649350 -0.047158125  0.4411675561  0.034351400  1.1480885618
## 935  -1.191110304 -0.473273896 -0.1938840616 -0.205030869  1.0495679112
## 936   0.322481974 -1.049617212  0.3917270455 -0.964930432 -0.0509581039
## 937   0.751407357  0.802392775  0.6887980684  1.584450282 -0.5011929930
## 938   1.879122011  0.912909892  0.8096627484  0.479761588  0.1688138394
## 939  -0.045753090  0.856202842 -0.0576050788  1.381704077 -1.7187132984
## 940   0.097992838 -1.194648215  0.0574414330 -0.368066004  1.1581425245
## 941  -0.223387837 -0.433118567  1.3876899786  1.947756801  0.1650904415
## 942  -0.029918846 -1.112188257 -0.5508302172 -0.686951040 -1.7862404594
## 943   0.057656479  0.339402207  0.1029540859  0.001698693  0.8705261880
## 944  -0.183167072  0.777354916  2.1572930686 -1.175511871  1.4779987989
## 945   0.131079390 -1.221593638 -0.5447528095 -1.195734339 -0.0383475836
## 946   0.981468841  1.128949702  1.3251502535  2.211890309  1.3536153575
## 947   0.247179529  0.383962643  0.7754529110  1.876944439  0.9102240110
## 948   0.250435901  2.409014398 -0.3811761228 -0.149927703 -0.1741069633
## 949   0.505795915 -0.187436019  1.5114752539  1.312014754 -0.9286139569
## 950   0.138505109 -1.048774296  0.0283738905  0.763391935 -1.4686272567
## 951   0.446644185 -0.276608873 -0.8035561540 -0.279429508  0.8162958033
## 952   1.192388124 -1.117101079  0.6939143918  0.266644588  0.3311785460
## 953  -0.753447082 -0.623001186  1.6549299541 -1.179844574  0.9142332694
## 954  -0.619669527  0.818098434  2.2046299642 -0.884142093 -1.4622985301
## 955   2.447601129 -1.578253150 -0.9503516797 -0.510747382  0.5745516795
## 956   2.742538091  0.146526676 -0.0793398674 -1.076909278  1.4304579705
## 957   1.656134866  2.038129653  0.6148118851 -0.179974048  1.2049092082
## 958  -0.758736737  1.408159849 -0.0313711893  0.214462557  0.7437480162
## 959   0.449535637 -0.887739772 -1.5076935539  0.147968981  0.9676302355
## 960   0.251524483 -0.550224464 -0.6438876970 -1.121168645  0.0714791444
## 961   0.150474488 -0.463653887  1.3197140271 -0.371442810  0.1408139665
## 962   0.010538799 -0.266899957  0.0994954784 -0.540284122 -0.1334479862
## 963   3.410463925 -0.910336076  0.7171401959 -0.127866616  0.1251939105
## 964  -0.029933833 -0.030011882  1.2932266842 -0.527546869 -0.3740353224
## 965   0.259647403 -1.059295193  2.3298662709  0.508883757  0.2953559852
## 966  -0.938683424 -0.988135482 -1.5322284042  0.919750136  1.5145306831
## 967   0.841169475  2.468382046  0.2952258629  0.520613793  0.4604259907
## 968  -0.618876269  0.774278147  0.6756388205 -0.721604353 -0.8325125808
## 969   0.332036550 -0.167967738  0.4514947126  0.694527719 -1.4871560938
## 970   0.913594150 -0.320409626 -0.6885157570 -0.911885261  1.0014236317
## 971  -1.418550828  1.084141508 -0.5732327076 -0.472434788  0.3765437432
## 972   0.825472458  0.534644249 -0.3774180998  0.610813362  1.5356898168
## 973  -1.381180836 -1.174530077  0.4280545620 -1.732626159  0.7774090462
## 974   0.239738379 -1.013681512 -0.6021200151 -1.170361421  0.8747396052
## 975  -0.449364690 -1.144268603 -0.6402452901 -1.372475343  1.4204173174
## 976   1.979009001  1.590062994 -0.9292067115  0.670173103 -1.4648840928
## 977   2.208542587  0.547248803  0.6650167794  1.575035860  1.2562217435
## 978  -0.544406201 -1.255633037  0.0309111131  1.490511481 -1.2201971079
## 979   0.379123187 -0.235637789 -0.0645983084 -1.187377445 -0.1530569895
## 980  -0.133123094  0.110960517  0.1339841442  1.890325217 -0.6289648349
## 981  -1.154561534  0.837302297  0.3160429694 -1.890128940  0.2621422486
## 982  -0.343913156 -0.222646271 -0.8185381595  1.455641096  0.8147047499
## 983  -0.442409515 -0.370442856  0.0202728370 -0.321050929  0.9981721728
## 984   0.747387542 -0.757218120  0.4159296249 -1.488097305 -0.2776080712
## 985  -0.537589775 -0.574206119  1.4827831018  2.232764813  0.1568869045
## 986   0.133085141 -0.365282113 -0.7482805067  1.889608786  0.8196452297
## 987  -0.024214941  0.328790053  0.3891398250  0.343492530 -1.8527919722
## 988   0.572584139  0.602710981  0.5722610947 -0.742384773 -0.5768884155
## 989  -0.028227481  0.203058515 -1.5505721969  1.414030237  1.1667150757
## 990  -0.635078083  0.362134352 -0.0730410511 -1.053657108  0.8249548813
## 991  -0.009720480 -0.177968946  0.2633051844 -1.752793922 -0.2164546834
## 992  -0.647317082 -1.214261855 -0.3167979562 -0.269354949  0.5951991618
## 993   0.454566443 -0.230846531  0.0484173298  1.365487289  0.4684472305
## 994  -0.736047158 -1.017868623 -0.8714699289  1.039625233 -1.1226106876
## 995   1.002749187  0.158932966 -0.9857238969  2.193746355  1.4678439389
## 996   0.985961567 -0.432505423 -1.8446680705  0.615688327 -1.5173924324
## 997  -0.261241346 -0.940034663 -0.5254387925 -0.270304068  0.9011100782
## 998  -0.454631786 -0.599865022  0.1963129004  0.883710987  0.7086987023
## 999  -0.636644254 -1.774765392 -0.6366019595 -1.325934740 -1.3588900687
## 1000  2.333482805 -0.827857534  1.4153249080  0.583388369  0.1405471579
## 1001 -0.628299702  3.086849692 -0.6430690389  1.057816201  0.6084320069
## 1002 -0.683419138  0.507424773  0.0271168594 -0.087666386 -1.4854461062
## 1003 -0.061618510 -0.555629559 -0.6172057381  0.364546560  0.3685552190
## 1004 -1.140134817  0.161836114 -1.5140179675 -0.925812096 -1.5173120138
## 1005 -0.518463033 -0.940452057  1.4474871275  0.269548552  0.0694926370
## 1006  0.114166811 -0.503125629  0.5283846537  1.755562207 -0.6539486423
## 1007 -0.160264433  0.429400387  1.2693616961  2.216492571 -1.1647635620
## 1008  0.198740159 -1.914328018 -0.5955223999  0.001276077  0.4155512389
## 1009  2.462309616  1.000665732 -1.6430980333 -0.930693933  1.3388325941
## 1010  2.008180210  1.006414311  1.2113657801 -0.612399495  1.3093979121
## 1011  1.499928823  0.653860715  0.2308373310 -1.803755225 -0.9307744952
## 1012 -0.013703814  0.668134265  0.7322251332 -0.573484854 -1.7142409263
## 1013 -1.082642889 -0.048151294  0.0802200011 -0.926494374 -1.0066428730
## 1014 -1.015807885  1.523039966  1.4214641018  0.057800818  1.1168344578
## 1015  0.426287849  0.819872656  1.7813619968 -0.513187352 -2.0034885350
## 1016 -0.872625106  1.113438567  1.3773923082 -0.486005032  1.0272434016
## 1017 -1.061642238 -0.464507256  1.6638510700 -0.502639390 -1.7085255823
## 1018 -0.720655411 -1.709367712  2.3036583327  0.006009542 -0.4466331243
## 1019  0.208708421 -0.134404567 -1.5056381984 -0.369322650 -1.8398791677
## 1020 -0.646369904  1.141469831  0.4672503825  1.591065380  0.2189526128
## 1021 -0.369250028  1.600450087 -1.6838089408 -1.035426644 -1.2629774272
## 1022 -1.009091369 -0.333360919  1.3946826508  0.196334657 -1.3081600505
## 1023 -0.326945682 -0.747404255 -1.8977087470  0.383819295  0.4377255291
## 1024 -0.157671630  0.369043320  2.0681926217 -1.116681323 -1.2790893841
## 1025  2.453721063  0.221360473  1.0118062766 -1.379892297 -1.8216071311
## 1026 -0.635943869 -1.634894139  0.0472980343 -0.808850052  1.3484956463
## 1027 -0.214912867  1.034903045 -1.4486951843 -0.094244356  0.7443788017
## 1028 -0.783903641  0.762780460 -0.2618804181 -0.350173214  1.2828409196
## 1029 -0.581613921  0.966867630 -0.8795357995  0.050710885 -1.0444169911
## 1030  0.020886846  0.291751210  1.0105215855 -0.582548523 -0.0832304429
## 1031  0.876231408 -1.317637658 -0.5656648308 -0.615714850 -1.5149612346
## 1032  0.663647562  0.450510946  0.2691845994 -1.087173125 -1.5558715821
## 1033 -0.702288098  0.220808317  2.2414232098 -0.938360912 -1.5740105229
## 1034  0.219892160  0.052405362  0.8313670170 -0.516011290 -0.3298358412
## 1035  0.651793083  0.309139568  1.3476644570  1.483882278 -0.5723396581
## 1036 -1.299505697  1.209287323  0.6653291527 -0.337931489  1.6039811621
## 1037 -1.164166010  1.064974096 -2.5125395814 -0.405600327 -0.4192254214
## 1038  0.285545991  0.485082328  0.3225921408  1.042230263 -0.6510318400
## 1039 -0.311822272  1.110591502  1.2442049295  0.034304092  0.4166380122
## 1040 -0.777137628  0.037510999  0.0883919420 -0.096936624 -1.8623668120
## 1041  1.013598159 -0.807752508  0.6263624225 -0.206617224  1.5390512739
## 1042 -0.142431834 -0.773841358  1.4283849550  0.015438000  0.9827213306
## 1043 -0.260817172  0.362731261 -0.0349553993 -0.633504613  0.2458172743
## 1044  1.470583396  1.116601131 -0.3592504665 -0.296642501  1.3647498877
## 1045  0.002020256  0.996789216 -0.9786868567 -0.111706187 -1.6430363761
## 1046 -0.501791481 -0.113049927  0.9256130119 -1.411852578  0.0975031207
## 1047 -0.191379945  0.035071300 -0.2679967563  1.825647125  1.1599038339
## 1048 -0.459385680 -0.588391558  1.3819445332  0.250031123  1.0039244295
## 1049  0.176939554 -0.148331618  1.3913952438 -0.215798112  1.1092377438
## 1050 -1.057990241  0.648061559 -0.9397676877  0.650271446  1.8306442335
## 1051  0.452588914 -0.936255461 -0.6693395843 -0.467954294 -1.4706888991
## 1052 -0.808291356  2.558094993 -0.9391772109 -0.642527577 -1.6436678328
## 1053 -1.160801208 -0.344139869 -0.8788527016  0.137828957  0.1679167231
## 1054  0.974896142 -0.389007532 -1.0946823466 -0.527791767 -0.4385944364
## 1055  0.795884832  0.936773044  0.6592809491 -0.098886541  0.1070285911
## 1056  1.108072012  1.127430596  0.5009678952  1.266486524 -0.3274681910
## 1057 -0.915211357 -0.211774077  1.0137520782 -1.592630996 -1.6764365819
## 1058 -0.808112358  0.829782121 -1.1270761050  1.343182961 -1.2801877824
## 1059  0.605206193 -0.865786461  1.8019939800  1.430831293 -2.0007479044
## 1060 -0.793891588 -1.090610820 -0.0510365131 -0.519438481  1.4260863318
## 1061 -1.411805921 -0.010827140  0.4860837733  0.815637280 -0.6064289444
## 1062 -1.208464805 -1.035104719  0.7524973469  0.494064681  1.1907608478
## 1063 -0.042350671  0.526850113 -1.0762047538 -0.825408429  0.0125722927
## 1064  0.361593444 -0.907127300  0.1674554269  0.953410324  0.0689219709
## 1065 -0.553615991 -1.073059339  1.0155351666 -1.412208387 -0.0666419234
## 1066  0.182045400  0.415799449 -0.0806644778 -0.551499519  0.8366186476
## 1067 -0.919874098  1.804412059  0.7316217283 -0.611306167 -1.5056564955
## 1068 -0.089145067  0.616616753 -0.9727162112  0.802511199  0.3563519285
## 1069 -1.631139133  1.035090074  0.3754354404 -0.191329941  0.7442945000
## 1070 -1.317106209 -0.165256143 -1.8287813178 -0.057036347 -1.5208288013
## 1071 -0.581547549 -0.730296593  1.4217836858  0.229474601  0.0994989861
## 1072 -0.265626028  0.741367298  1.1855039835 -0.467074503  0.6274909024
## 1073 -0.733009361 -1.525492698  0.6514577898 -0.727021297  1.3713322326
## 1074 -0.123827670 -1.377068621 -0.1759364543  2.606938070  0.6253298592
## 1075 -0.638898204  0.642568511  0.1328028496 -0.140763522  0.6201787789
## 1076  0.330503289 -0.546056792  0.3847064385 -0.877296005  0.0394459006
## 1077  2.064550012  0.718600131 -0.6456336770 -0.231234432 -0.8278729238
## 1078 -0.931764815  1.399738189 -0.4601395116  0.445652856 -1.4483831194
## 1079  2.299859908 -0.237176644  2.3927868882  1.926366701  1.1049000572
## 1080 -0.287791901  0.742568722  0.6600785179 -0.380860973 -0.5415569039
## 1081  1.487024837  1.431356941  1.5945992451 -1.299098576  0.4577639308
## 1082  0.447091161 -0.331146889 -1.1182594275  1.905417244  1.1763820104
## 1083 -0.896479817 -1.846628651  0.0981301104  0.886247267 -1.3290432510
## 1084 -0.713452894  1.064095799 -0.5278114304  1.435312794  1.1267243231
## 1085  0.352894575 -0.718329767  0.0683492678 -0.941986229  0.9564635676
## 1086 -0.423019330 -0.402566284 -1.8125233303  0.249241292  1.1108408985
## 1087  3.443524181 -0.419945935 -0.4579918060  1.310923035 -0.3686748127
## 1088  0.019729453 -1.374552960  0.0417237906 -0.341747082 -0.6485095196
## 1089 -0.606532693  0.844363158  0.6124512209 -0.770043901  0.3438435621
## 1090  0.191191416 -0.668978415 -0.5835083801  0.028595968 -1.6993280176
## 1091 -0.002156663 -0.754133206  1.3494800612  0.031067903  0.6827679527
## 1092 -0.360530034 -0.531527238  0.7824407687  1.873976798  1.0227077603
## 1093 -0.280653923  0.441587275 -0.6321338450  1.543809471  1.1538479080
## 1094  1.566337526 -0.358000329 -2.4943992183 -0.109982964  1.1380129843
## 1095  0.226330494 -0.934246875  2.2549673884 -0.153172200 -1.4727105667
## 1096  0.569847362 -0.626504472  0.2182809812  2.053272007 -1.0306846502
## 1097  2.395811948 -1.354317201 -0.5948428415 -0.770990222  0.2694049659
## 1098 -1.172525845 -1.177853332  1.4383157685  1.636594828  0.3093389293
## 1099 -0.473532069 -0.161977751 -0.7023375247 -0.682666882  1.2985071582
## 1100  0.620851476  0.255190390  0.6783120161 -0.657288245 -1.7924490920
## 1101 -0.411969665 -0.406448435  0.1567300688  2.022559233 -1.0282357140
## 1102 -0.224908694 -0.434207954  0.6918919709 -0.423244920  1.3094719569
## 1103 -0.765480244  0.593747905 -1.5534408817 -0.656209428  0.0355789600
## 1104  0.146929331  2.028368732  0.0137454898  0.433567523  0.2991616985
## 1105 -1.370355936  0.911543669 -0.8774946333  0.149701473  0.4097002903
## 1106 -0.759328115  0.821084601 -0.4781967343  1.247547363 -1.5674088185
## 1107  0.354469777 -0.567727457  1.4193300013 -0.458822821 -0.7372774418
## 1108 -0.079789226  0.480436261  0.0798376700 -0.021212443  0.0051603122
## 1109 -0.735715291 -0.212395608  1.3355307225 -0.424778409  1.0576656796
## 1110 -0.199651979  0.347566967  0.8592741220  2.243881276  0.0329526309
## 1111 -0.991639897 -0.030630153  1.3269059420 -0.394623586 -1.5675014150
## 1112  3.235116452 -0.584063758 -0.5470427886 -0.746768511 -0.4339452252
## 1113 -0.393833619  0.529679776  0.6611636306 -0.730297626  0.3020758634
## 1114 -0.678150632  0.868902231  0.4614963081  0.051808500  1.0437733785
## 1115 -0.409544586  2.369024218  0.3710657724  1.392041248  0.4441439700
## 1116 -0.946583598  0.309443148 -2.4707851040  0.383669604 -1.7318226758
## 1117  4.435142427 -0.383428238 -0.4563051278  1.727107609 -0.3404952715
## 1118 -1.013321991  2.169753619 -1.5581983320 -1.046384693 -0.5500303640
## 1119 -1.132964942 -0.667303818 -0.5716794221 -1.093889016 -1.7318328379
## 1120  0.684619340 -0.669899540  0.7398313242  0.700884606  0.1143426801
## 1121 -0.423102995 -0.076123476  1.6466496396  0.322006538 -0.7370373068
## 1122 -0.701543376  1.462214170  0.0372887041 -1.169615226 -0.7190694138
## 1123 -0.138249460 -1.386534294  1.3408319500 -0.377814766 -0.3266120686
## 1124 -0.286109962  0.483811237  0.0977883846 -0.069347640 -1.7628418055
## 1125  0.316905508 -0.158854609  0.0313360046 -0.487354563  1.0549197294
## 1126  0.112302716 -1.618980074  0.3018035032 -1.878923854 -1.3698646037
## 1127  1.084911031  1.118395583 -0.0542052160 -0.421574255  0.4022005560
## 1128 -1.177187707 -0.580475724  0.1354191524 -0.039293006  0.9729563710
## 1129 -0.576115508  0.819285001  1.3825944421  0.031649255 -1.6759496574
## 1130  0.698329717  1.356954003 -0.7004398243 -0.909835688  1.6073228758
## 1131 -0.027778487 -0.561785428 -0.8094476645  2.421847064 -0.7032445612
## 1132 -0.071210588 -0.143990292 -0.8210032004  0.595188160  0.8334712826
## 1133 -0.174199165 -0.509894058  1.3097419427  0.872720005  1.3081778963
## 1134 -0.147484938  0.814961485  0.7029232006  1.928993470  1.2707463802
## 1135 -0.819982486 -0.625878410 -1.6136851055 -0.237642933  0.3775837011
## 1136  2.819466242  0.010717155 -0.4703495715  0.712289321  1.0052811445
## 1137 -1.052468566 -0.518182866  0.7966474649  1.730605475  0.1291363484
## 1138 -0.985493774 -1.141387894 -0.7809249493  2.082247815 -0.5348293445
## 1139  2.847096429  0.042411283  0.1738460792  1.317705912 -1.1621330376
## 1140 -0.762844363  0.317533389 -0.5659417232 -0.846539399 -0.9428697296
## 1141  2.815009707 -0.928161807 -1.5158168370 -0.086219758 -0.7635358624
## 1142 -0.722799443 -0.413749784 -0.1987824325  0.426803086 -0.6935073942
## 1143  0.453652558  0.634659991  1.3873792769  0.184720296 -0.2156514702
## 1144  0.336473189 -0.110112921  1.3675276674  2.224798958 -1.5297068901
## 1145 -0.774143094  1.493027001  1.4074878992 -0.464121414  1.1106973211
## 1146 -0.878140561  2.066219669  0.0674684754 -0.052580470  0.2960237127
## 1147  0.081696858 -0.420662959 -0.5301490195 -0.173319272 -0.1712069658
## 1148  0.217773861  0.534132546  0.4226486698  2.732459830  0.1162485998
## 1149 -0.087701415  0.820446993  1.4330250264  0.641460311 -1.0618328700
## 1150 -0.459095273 -0.713471362  1.4764012997  1.529517097  1.0123039458
## 1151  0.600069380  0.008852374  1.5311415237  1.622043128 -1.1708449874
## 1152 -0.554797718 -0.637441729  0.5428407350  2.844837332 -0.6860779400
## 1153 -1.050564649 -1.694889864 -0.5993702466 -1.009767600  0.4273147850
## 1154 -1.411821244 -1.482085388  0.3918218204 -1.647376330 -0.7621140707
## 1155  1.461819595  0.868026119  0.0859323942  1.579125271  0.9942484860
## 1156  0.173668382 -1.168011828 -0.0122276381 -0.768699672  0.2618771475
## 1157  1.500140818 -0.758570121  0.1044780939  0.532295412 -1.6619216137
## 1158  0.426871203 -0.493295623  0.1333113537 -0.066381688 -0.1550423233
## 1159 -0.359232351  0.293125041 -0.8795747549  1.326982760  0.3128468501
## 1160  0.089205789 -0.351185439 -1.8612025401  0.336055488 -1.5331507733
## 1161  0.619603383 -0.807908849 -0.7167165499 -1.192987064  1.1916814454
## 1162  0.086595285 -0.374878550  0.9187301596 -1.543039679  1.2359278118
## 1163  0.397582468  1.455249765  1.3993412924  0.253654382  1.4284484407
## 1164 -0.236706033 -0.080270984 -1.1777931975  1.232895548 -0.5736881394
## 1165 -0.195942404  1.096903946 -1.5748583938  0.598143001  0.4413603623
## 1166  0.335023234  1.142496829 -0.6011545769 -1.213031612 -1.9501076737
## 1167  0.853866344  1.107392945 -0.6287663547 -0.929389006 -0.1967404555
## 1168 -0.789487509  0.685074185 -1.5950846416  0.369556934 -1.1265931777
## 1169 -0.603758989 -1.675502510 -0.6156729958 -1.343391349 -1.3318427061
## 1170 -1.167164892  0.894855900  0.0878633177 -0.493819046 -0.5206165075
## 1171 -0.882443758 -0.434624640 -1.5151949155 -0.667212472  1.0252912798
## 1172 -0.835325668  0.846911555 -0.5813790358  1.061655332 -1.2885036496
## 1173 -0.809187609  1.374741468  0.0867539010 -0.339918560  0.4648981595
## 1174 -0.384864725  1.064630299  1.3825302735 -0.113773336 -0.7422882314
## 1175 -0.341632107 -1.670265404  0.0439102913 -1.014147855  1.3462078867
## 1176 -0.283822229  0.504606372  0.6867289983  0.354842308  1.1948019426
## 1177  1.022131923  1.175572794  0.7012180647  1.377485196 -1.5993588923
## 1178  1.464912984  1.661564069  1.4079699608  1.302927657  0.8978661315
## 1179 -1.176071956 -0.882457735  0.1376159895 -0.879878548  0.0258363231
## 1180  0.237298231 -0.676490928  0.7329230125 -0.433835195  0.9860541828
## 1181 -0.719920148  0.016214474  0.6868398795 -0.143202824 -1.5627164221
## 1182  1.836593939 -0.801379401 -0.0833635242 -0.667675034  0.6430065398
## 1183 -0.377269882 -0.256502837  0.0606314477 -0.858263087  0.7291632457
## 1184 -0.402724879  0.685050839  1.2958621716 -0.511218544  1.5266312571
## 1185  1.832848729  1.339177615  0.0736698661  1.255984261 -0.9727763157
## 1186  1.985906235 -0.862664800  0.0402447213  0.386652214  0.3690019053
## 1187  0.244734812 -0.158093644  0.4168749881 -0.486055156  0.7183519181
## 1188  0.268408184  0.560728294  0.3139697385 -1.890025367  1.1266283131
## 1189 -0.245106676 -0.564788273 -0.1764266804  0.212458117 -1.5916283497
## 1190 -0.122463640 -0.332434234 -0.5578909170 -1.040942670  0.7123745324
## 1191 -0.005695705 -0.755235377 -0.2055564430 -0.030425704  1.0178806789
## 1192  0.099014452 -0.482278826 -0.5179814796 -0.743614536 -1.9505090555
## 1193 -0.597733485  1.225396689  0.3135040162  1.528940139  1.3802291708
## 1194 -0.513343482 -0.253387931  0.6616560165 -0.582773588  1.0320749989
## 1195  0.637839257  1.942762103  0.6399183008 -0.859592260 -0.5988557380
## 1196  1.246656623  0.777652990 -0.0504601480 -1.179310147  0.3438342053
## 1197 -0.171282288 -0.045334079  0.0015386266  1.166311903  1.3633756002
## 1198 -1.228542370 -1.470532332  1.3939545595  0.256864329  1.4163546490
## 1199 -0.121337931 -0.711207982 -0.5555028347  0.348641268  0.0597804779
## 1200 -0.720081687  1.486171935 -0.8247282534  2.001518731 -1.5103673356
## 1201 -0.530088251  0.657785603 -0.7210712525 -1.398688249  0.2676537739
## 1202 -0.675774685 -1.684347111  0.0674888906 -0.378863423  1.3453762377
## 1203 -1.139040089  1.154241020 -1.0099571035 -0.514850323  1.6058088542
## 1204  0.357842610  1.001332299 -0.6591724257  1.144355093 -0.8040177445
## 1205  0.235675821 -0.335188682 -0.0811993210 -0.411232693  1.2937542153
## 1206 -1.055550836  0.020076408  0.7347799216 -0.508168920  0.7943438714
## 1207 -0.520116170 -1.034016716 -0.5298269996 -0.554270147  0.8781088667
## 1208 -0.136734813  1.439580542  0.5783920981  1.315119536 -1.2949391778
## 1209  0.572012439 -1.534211375  0.3412176910 -1.331752622 -0.7362414617
## 1210  0.742958127  1.284371914  0.1549389794 -1.848424446  0.0405491900
## 1211  0.129491396 -0.852968329  0.8015554888  1.506094122 -0.7877142576
## 1212  0.290857319  0.041628382 -1.5303300831 -0.717236028 -0.0488941383
## 1213 -0.001565408 -0.839605085 -0.5429867442  0.704674350 -0.8377737309
## 1214 -0.993777009 -0.939381127 -0.5246819720 -0.606048725  0.0016755368
## 1215  0.599080546 -0.338998387 -0.6726564118 -1.160755855  0.1090490211
## 1216 -0.120324163 -0.539904894  0.3671851894 -1.558556401 -2.0386268400
## 1217  0.750702731 -0.494727700 -0.6554774800 -1.120858543  0.9717786634
## 1218 -0.633600836 -0.875457028  0.1445916206 -0.121343968  0.0441288360
## 1219  0.784723593 -0.465052684  0.0336669147 -0.431700361  1.0063353889
## 1220 -1.075789231  1.690964266  0.1188739963 -0.314226418  1.1175989106
## 1221  0.249128583  0.180929481 -1.5066168955 -0.580970653 -0.0070517106
## 1222  1.931766175 -0.876270760 -0.9893593774 -0.649252882  0.6983947242
## 1223 -1.186047466 -1.538581218  0.0814953760  1.101106093  1.3731940852
## 1224  1.895418044  1.120151548 -1.8513656171  0.695520822  0.5679058024
## 1225 -0.837824174 -0.585349673  1.1283867672  0.351508654  0.6447709777
## 1226  2.544926295 -1.066752080  0.7519771999  2.137850028  1.2695088876
## 1227 -0.883553378  0.921380326 -0.8803753641  0.240888848 -1.3453386860
## 1228 -0.468787002 -0.368130166  1.0508855456 -1.289435407 -1.1008696453
## 1229 -0.432245282  1.244524082  0.6325461804 -0.627676891  0.4319820012
## 1230 -0.436056910  0.019344123  1.2730699688  0.099430047 -0.3787723004
## 1231 -0.581513653 -1.643132966  2.3895514824  1.888433227 -0.4004158124
## 1232  0.235857986  1.461060519  0.6904367788  0.488717291  0.2145694329
## 1233  0.097796931 -0.007534367  0.1673481194  1.860467426  0.8287145796
## 1234 -0.199809433 -1.551408443 -1.5485160591  0.700939670 -0.3495101698
## 1235 -0.771356791  2.492613709 -1.2866256971  0.173218689  0.4668068502
## 1236  0.814608076  0.602142013 -1.6294381411 -0.792577864  0.3461077782
## 1237 -0.697629260  1.695876130  1.4372458195  0.797321400 -0.9043606130
## 1238 -0.967816814  0.758882906  0.6394952651 -1.099176697 -1.1459732044
## 1239 -1.129670885 -1.130238757 -1.1899390943  0.408831759  0.6746236455
## 1240 -0.367658358 -1.118499625 -1.5486717761  1.492613529  1.4987811932
## 1241  0.410198911 -0.603474690 -0.6343598548 -1.221789922  0.9490912892
## 1242 -0.202346529  0.270623589 -1.7765465843  1.808224322  1.2577153481
## 1243  2.527587752 -0.190017475 -0.1337977012  0.493673232 -0.8690306820
## 1244  0.414548031  0.547487636  0.9111576725 -1.323583006  0.2379026809
## 1245 -0.091939338 -0.520829216  1.4533345330 -0.153697092  0.7455814310
## 1246 -1.030676599 -1.060352006 -0.5261512607 -0.296756096 -1.7907239499
## 1247 -1.071056295  0.717234147 -1.5339412997 -0.200000721  0.3608501001
## 1248 -0.084151977 -0.513075023  0.0837183469 -0.629414321 -1.6633666590
## 1249 -0.580110526 -0.755295432 -1.4834423532  0.003191177  0.0963326616
## 1250 -0.950790547 -0.442603027  0.7454624146  0.111574643 -0.7585059816
## 1251 -0.801149749  1.036537934  1.0002643713 -1.753109828  1.2165477912
## 1252 -0.151306865 -0.647407410  1.4020453561  0.926509871  0.4215872817
## 1253 -0.362437768 -0.531106075 -0.5726394697 -0.990752292  0.6661464254
## 1254 -0.310526465  1.254950465 -0.2303753268 -0.319203162  1.4000466609
## 1255  0.165491746  0.604555907  0.2773400054 -0.659223863  0.8248219976
## 1256 -0.623271114  0.367123358  0.4482669829  1.490296330 -1.4116129986
## 1257 -0.607193078  0.261736411 -0.3264272449 -0.300548475  0.5872844664
## 1258 -0.480717334  0.250039283  0.1388451614  0.561023340 -1.8031617474
## 1259 -1.115110930 -0.354695892  1.3831250194 -0.114033341  1.0350026595
## 1260 -0.300519658 -0.243774792  0.1237122176  0.555224811  0.1729714466
## 1261 -0.516336026  0.090821523  0.7681367408 -0.223808118 -0.9361618794
## 1262 -0.475568765  0.229190100 -0.6160357905  0.411152860 -0.6663288726
## 1263 -1.027179508  2.002127223 -0.0262893675  0.388517467  0.5569209940
## 1264 -0.780214360  1.854825719 -0.3022656935  0.666263377 -0.2768198481
## 1265  0.871369371  2.554781826  1.1863053405 -0.783480182  0.6940607447
## 1266 -0.497196523  0.545065379 -0.2279126150  0.009776879  1.2593125278
## 1267 -0.407607537  0.296143852  1.3617435149  0.511906615 -0.0064859949
## 1268  0.493498933 -0.982617891  0.1114364577  0.091461177  0.9290805991
## 1269  0.603846444  1.716563754 -1.0152205975 -0.672998423 -1.5065784542
## 1270  0.277583915 -0.674445278 -0.6677660855 -1.096409025 -0.8419068936
## 1271 -0.598593045  0.167646900 -0.6726628042 -1.305535942  1.3642890044
## 1272 -1.280954850 -1.421143790  0.7161249134 -0.279099351 -0.3693912335
## 1273 -0.250235707 -0.771130176 -0.0170804342 -0.515796996  1.2114506182
## 1274 -1.302155850 -1.321227628  1.3691840609  0.121283314  0.5524381682
## 1275  0.311014347 -0.640545336 -0.4334056625  1.840525406 -1.9420770925
## 1276  0.675241849  0.635190777 -0.0859677300 -0.966750577 -1.4746978261
## 1277 -0.310346349 -0.641156721  0.6573854624  0.031998784 -0.5083612464
## 1278  0.893934150  1.992344876 -0.6665487209 -1.456758501  0.2612810755
## 1279  0.272879341  1.003304561  1.3889834035  0.337512542  1.3356928580
## 1280 -0.342693539 -0.250762992 -0.3722490874 -0.305011490  0.4792930920
## 1281 -0.020555162 -0.466549687 -0.2727038445  0.441895148  0.4751126371
## 1282  0.338474734 -0.839980677 -0.5183705895  1.555508159  0.0612882039
## 1283 -0.433071487  1.058890341  1.4303369624  0.277928923  1.0466809627
## 1284 -0.631026149 -0.990637103  0.3705906687 -1.720283387 -0.0677123262
## 1285  0.272038586  0.581123684 -0.0552917995 -0.519830669  0.8840310028
## 1286 -0.301038060  1.592630481  0.6140775194  1.512285602 -0.0794398031
## 1287 -0.671124611  0.529242925  0.3088372680 -0.056679879  0.6493465722
## 1288 -0.799719778  1.416328937  0.3525346105  1.091746277 -0.3498716225
## 1289 -0.036012659 -0.713933787 -0.6552834198 -1.291071916 -0.5575720173
## 1290 -0.203548250  0.582175054  0.6771042561 -0.736609064 -1.4422274816
## 1291 -0.397196299  0.883530262  0.4780987977  0.903872821  1.0602033501
## 1292 -0.057642747  0.240794165 -0.4685582081  1.649081703  0.9966207144
## 1293 -0.441182163 -0.088258441 -0.6131352314  0.706463649  0.1602391682
## 1294 -0.690663698  0.882707164 -0.9749681876  0.191606645 -1.3748789622
## 1295 -0.378556876  0.830262740 -1.2463111379  0.547609804 -0.4245454049
## 1296  2.027824683 -2.086828019  0.9475564241 -1.192604965  0.3722419816
## 1297 -0.283940092  1.422475604  0.0941623992 -0.395633191 -1.2833193763
## 1298 -0.728769561 -1.412013743  0.7793217576  1.314640125  1.1397627131
## 1299  0.711741653  0.054539594  1.5899313498  0.740567789  1.3660352979
## 1300 -0.084989365  0.410986479 -0.6693475293 -1.395709618  0.2413591158
## 1301  0.308559602 -1.042898398  0.0474263180 -0.320143656 -0.5800499351
## 1302  2.144928430  1.063549738 -0.3711185047 -0.276094144 -0.3985801666
## 1303 -0.320520889 -0.551481316  1.0872293942  0.997260970 -1.1134873707
## 1304  1.598214918  1.194518241  0.6687593096 -0.570347730  0.4825733803
## 1305 -0.130127142  0.104603092  1.3476869604  0.686659573 -0.6269329530
## 1306  0.495846394  1.311533253 -1.6556699330 -0.154543810  1.0606903940
## 1307 -0.279589863  0.409562258  1.4373293452  0.147434985 -1.7384851179
## 1308 -0.860637767 -0.421603628  1.3925231413 -0.448726764  0.1440324149
## 1309 -0.315103697  0.420429307 -1.5565883120 -0.654022608 -0.8757872306
## 1310 -0.497730192 -0.907517009 -0.5250123005 -0.289990208  0.0187459574
## 1311  1.163477746  1.240489472 -0.0564736304  0.375390452 -1.6332643845
## 1312 -1.671192990 -0.556452936 -1.7121871218  1.353594987 -0.6840674032
## 1313 -0.898711369  0.162225894  1.4983824233  1.588001943  0.5803212018
## 1314 -1.224310338  0.452561188  1.4047120331  0.677837833 -1.4515024535
## 1315  0.215650242  0.759726991  0.9483578256 -1.383839438 -0.0083623896
## 1316 -0.576449868  0.979792650  0.7061840398 -0.674161442  0.9798545274
## 1317  0.231471551  0.088425980 -0.6346383724 -1.103884221 -1.8704430608
## 1318 -0.688365595 -1.372814500 -1.5365354371 -0.346281421  1.1406134004
## 1319  0.136990178 -2.027773935  0.3715087328  0.194903515  1.2377127402
## 1320 -1.060812668  1.498944597  0.3719059192 -0.990652090  0.9958126669
## 1321 -0.331494589  0.762787861 -0.9044138625  0.489997213  0.0997918895
## 1322 -0.595978606  1.239823941 -0.0241580164 -0.198307303 -0.7683061963
## 1323  0.642763877 -0.029997185 -1.6746213888 -0.815244597  1.3903350579
## 1324 -0.803752723 -1.107243695 -0.6230966309 -1.343326719  0.2418699953
## 1325 -0.467613589  0.205090869  0.0788104010  1.588924997  1.7317283817
## 1326 -0.699016687  0.724932329 -0.0315291872 -0.381166582  1.1903531859
## 1327 -0.604217033  1.785200865 -0.2072858273 -0.334157553  0.3115328228
## 1328  1.863672464 -0.063479609  1.3416004059 -0.266029157 -1.5084605397
## 1329 -0.268546943 -1.691891500  0.0979170022  1.220211910 -0.3980626269
## 1330 -0.987804942 -1.197341784  0.6516635993 -0.352975406  1.4312900641
## 1331  1.911067929  1.076939867  0.0449025550 -0.757366431 -1.3229692445
## 1332  2.787410644  0.218340047  0.7136309526  0.167007680  1.2071678401
## 1333 -0.978759016 -0.929450680 -1.5121792465  1.607873602  1.2342389985
## 1334  0.295350522  0.941810651  0.6384772439  0.085967202  0.3946165816
## 1335 -0.414506934 -0.791397357  0.5226455050  1.622956420  1.0454804054
## 1336 -0.806462175  1.794851302 -0.5936948323  0.478211205  1.1120140570
## 1337 -0.174369883  2.190748676  0.1802845176 -1.845430523 -0.6685711604
## 1338 -1.067486608 -0.416970105  0.7302869137 -0.538903406 -0.7634753482
## 1339 -1.148426529 -0.420771087 -1.5313484634  0.061272155 -0.7475698134
## 1340 -1.233596588 -1.454901735  0.7093835780 -0.237084952  1.3918281030
## 1341  0.254491804 -0.246856388  0.1172156994  0.076874236 -1.0017415553
## 1342 -0.016118767 -0.837788756  0.1442714877  1.075034538 -0.8114871971
## 1343  0.159782501 -0.305228716 -0.5992124014 -1.019285492  0.1235182312
## 1344 -1.064598354  0.065959591  1.3948842616  0.148070905  1.1242365870
## 1345 -0.561833293  1.170354440  1.3798237998  0.151105283  1.0478450112
## 1346 -0.373531215 -0.970363929  0.6928433017  0.838738433  1.2052726102
## 1347  0.540536221 -0.861227934 -1.5920649170  1.741649936 -0.5079609424
## 1348  0.056750090 -1.285134489 -1.6380054381 -0.809733114 -0.3232647504
## 1349  2.013115732  0.123366021  1.4314458211 -0.416931993 -1.7473654229
## 1350 -1.149068150 -0.792545959 -0.9042879239 -0.622356318 -0.5164291639
## 1351 -0.148422971 -1.254942627 -0.8689554818 -0.464640531 -1.4592015652
## 1352  2.721244943 -0.301173311 -0.5659450422  0.966597193  1.0833669506
## 1353 -0.395922929  0.869268711  1.3020319001 -0.455466459 -0.8021005773
## 1354 -0.590409380 -0.011040050  1.4400534028  1.286924370  0.8378661771
## 1355  0.139420929 -0.144463380 -0.7689526104  1.059803137 -1.3456314837
## 1356 -0.473712133 -0.100419155 -1.2044954658  1.826907482  0.5924560655
## 1357 -0.393164373  0.873709374  0.6523699015 -0.126198626  0.3703322556
## 1358  0.953398456  1.614360854  2.2830199190 -0.714695591  0.5138497701
## 1359 -0.214935993 -0.824635813 -0.6042729330 -0.436687012  0.3166165603
## 1360 -0.183456679 -0.624500126 -1.6399573692 -0.826897973  1.5621348728
## 1361 -1.242703332  1.551343552 -0.9092952289 -0.508703594 -1.2423134666
## 1362 -0.483634223 -1.254847152 -0.5307649550 -0.642952566 -0.0492937967
## 1363 -0.190300939  1.131808464 -0.0179044970 -1.061282253 -0.7846906593
## 1364  0.069562708 -0.193974533 -0.8052379033  0.569517031 -0.9367707958
## 1365 -0.074093593 -1.246569055 -0.5969048103 -1.341595098  0.2356904185
## 1366 -1.192830336 -0.389040643  1.4434476399  2.012174208  0.1687350096
## 1367 -0.525189061  1.450006107  0.0823295770  0.972610002 -1.5784729855
## 1368 -0.906258650 -0.093886054 -0.1541534652 -0.027136486 -0.9243292453
## 1369  0.704376641 -0.705458381 -0.4642330643  1.155548867 -0.1879915228
## 1370 -0.326002655 -0.461857745  0.0786321311  0.085459208  1.2919933798
## 1371  0.048695428  1.931911837  1.6165005164  0.011760425  0.2448191961
## 1372 -0.228664786  2.175644209  1.2674554690  0.633710936  0.9211625521
## 1373  0.198435667 -0.638043766  1.3218699562  0.318406720 -1.3582936606
## 1374  0.807608522 -0.957101308  0.7483556284  0.206570270  0.9578748799
## 1375  1.203857219  1.383912665 -1.6851033945  1.104095654  1.3736161461
## 1376 -0.814896500 -0.333295166  0.0114562622 -0.754775588 -1.3596899944
## 1377 -0.117816209 -0.711627453  0.2782104145 -1.043622616 -0.6113020004
## 1378  1.457200168 -0.133998699 -0.7888148514 -1.560263419 -0.1627017534
## 1379 -0.522393026  0.797916045 -0.6316422829 -0.149115833 -0.8613538951
## 1380 -1.079884065 -0.476467009  0.7975982235  1.472686955 -1.6328011474
## 1381 -0.370969815  0.178716034 -0.4443240362  2.446885657 -0.7845843868
## 1382 -0.787496282 -0.607602787 -0.8155303839  1.130848732  0.1469017648
## 1383 -0.650444971 -0.898025670  2.2831523103 -0.800259594  0.2888174540
## 1384 -0.503096351  0.085115759  0.7431662557  0.199383576 -1.8273056547
## 1385  0.872128518 -0.706355689 -1.5141322229 -0.773904047 -1.6442900789
## 1386  0.275518500 -0.125915781 -0.8036377131  0.886053136  0.8471949959
## 1387 -0.672428242 -0.765371894  0.4811712980  0.122457757  0.1450124374
## 1388 -0.543834788 -0.484695144  0.4528450865  0.039476327 -1.5767291483
## 1389 -0.355473156  0.708796313 -0.5236953835  0.156030019  0.0407393925
## 1390 -0.029058707 -0.635818967  1.4026590197 -0.379065879  1.0094740968
## 1391 -1.038817244  0.361601866 -1.4861215154  0.801014175  0.3086645293
## 1392 -1.077642755  1.021942613  0.3467534942 -0.138117772 -1.3213638081
## 1393  0.236474864 -0.414601649 -0.5422216139 -0.489884686 -0.1712039104
## 1394 -0.338637736 -0.992383640 -0.5280031778 -0.354192236  0.8901476697
## 1395 -0.579877431  1.672063589 -0.5743094931 -1.069865790  1.0856744802
## 1396  0.152222927 -0.544912020 -0.4511287173  1.500376233 -1.9341508629
## 1397  0.114403539  2.392175371  0.3568506803  2.263655945 -1.3190793805
## 1398 -0.158832526  0.612398019 -1.0943276670  0.137937417 -1.1497667209
## 1399  0.148952222 -1.107679837  0.0476630685 -0.387123967  1.1720809407
## 1400  0.635798543 -0.319148789  0.0274798544  0.053852506 -1.6186879246
## 1401 -0.242042253 -0.219958913  0.7122068457 -0.549783822  0.7595634850
## 1402  2.002521745  1.337389850  0.6977675459  1.829873478  0.2231311415
## 1403 -1.003494900 -1.332341078 -0.6957015740 -1.311196483  1.3575948361
## 1404  1.895515445 -0.573947415  1.4872959642  1.216766464 -0.9770870099
## 1405  1.220859999 -1.314376193  0.0706769916  1.429116580  1.1758246552
## 1406  0.618144838 -0.221175383  1.0691837257 -0.625913580  0.1390774359
## 1407 -0.088120260  1.696929608  1.2106488813  0.308550241  0.5313626746
## 1408 -0.798598246 -0.979802216 -0.8719617786 -0.607455236 -0.5367860314
## 1409 -0.682694673 -1.602844841  0.4062048568 -0.612049266  1.0081231085
## 1410  0.558773869 -0.700762003  0.9967110930 -0.360227244  0.9128078098
## 1411  0.295383114 -0.241257596  0.6342404775 -0.754221417 -0.4244302824
## 1412 -1.301129148  0.169444885  0.7451322444 -0.723677149  0.2353728419
## 1413 -0.036069050 -1.077012972 -0.2278671084 -0.220254360  1.2496298839
## 1414 -1.247326313 -0.015067150 -0.9413711664 -0.753799794  1.6909888830
## 1415  1.419878921 -0.250194510  0.0695416033  1.562654122 -1.5677070266
## 1416 -1.021639246 -0.547601716 -0.9616104581 -0.620800417 -0.4802475579
## 1417  0.649752690 -0.593196928  0.7538563602 -0.480198557  0.7204789160
## 1418 -0.780983991 -1.043223360  0.0119852913 -0.982326996 -1.5010446692
## 1419  0.030395129  0.211835569  0.0755235909 -0.426937261 -1.8147247347
## 1420 -0.496378152  1.788315264  0.4245699741  1.754040056  1.2233838479
## 1421 -0.333902927  0.126699460 -0.6815699479 -1.306152190  1.0646968691
## 1422  1.329506355 -0.875861085 -1.3240690428  0.123669317  0.7373989381
## 1423 -1.049991167  1.511082599  0.0705037710 -0.053131908  1.0694118695
## 1424 -0.818266688 -1.669100876  1.0330022109 -1.501456307  0.9960764013
## 1425  0.166745637 -0.284205190  0.1206769833 -0.024335299 -1.0099392420
## 1426  0.127722175 -1.433017050 -0.5855102435  0.203326375 -0.6683043380
## 1427 -0.466067658 -0.230227650  0.8440748671  2.391202582 -0.0830130376
## 1428 -1.165536432  2.181318622 -1.6143545750 -1.016970229 -1.4480597758
## 1429 -0.867248658 -0.202486671  0.7392970045 -0.615911483 -1.0131667699
## 1430 -0.336592155  0.304234339 -0.6779526017  0.770012195 -0.9445254797
## 1431  1.594207673 -0.312855580  0.1051566529 -0.080327459 -0.6930160820
## 1432  0.966525516 -0.635413791 -0.5089458998 -1.136109664 -0.1952063552
## 1433  1.628867411 -0.912140628 -0.5449114852 -0.275757415  0.0559157211
## 1434 -0.602222403 -1.229192368 -0.8504786015  0.164713858 -1.4563811096
## 1435  0.384109584  0.648449789 -1.5652828560  2.261172828 -1.6856538516
## 1436 -0.571522947  1.116204399 -0.7211940078 -1.471938920 -0.5258170706
## 1437 -1.256712127 -1.390961219  1.3718087767 -0.189338854  0.5396549995
## 1438  1.280412970  0.019188740 -1.5420898195 -0.052488424  1.1421214695
## 1439 -1.395844572 -0.425994502  0.4999143356  0.916943973  1.0865533495
## 1440  0.438111521 -0.864092722 -0.6010704859 -1.038282089 -1.7452617713
## 1441 -0.662011521  0.866245900  0.6302903157 -0.709061318  1.5369328384
## 1442  1.109563242  0.505372842 -0.9999705967 -0.372094083  0.0512545151
## 1443 -1.103195273  1.693937879  0.3704194937 -2.033559090 -1.6230772199
## 1444  2.369229469  0.439769879 -0.8749142645 -0.559738575 -1.3768805846
## 1445  0.032592871  1.778828381 -2.0508428483  0.338703109  1.7878190589
## 1446  2.030759043 -0.608733942  0.8547906265  2.310945922 -1.8717001180
## 1447  0.201097943 -0.717671825  0.1445396772  1.929611111  0.9854412630
## 1448  0.663766634 -0.486615008 -1.4478907436  0.917256892  0.7772914411
## 1449  0.209243160  0.150257162  0.6558296526 -0.583064295  0.2358960174
## 1450 -0.743728136 -0.366209395  1.3666407353 -0.306037252  1.0367480286
## 1451  0.536285859 -0.401850049 -0.4782803927  1.501937103 -0.1402835692
## 1452  0.323489799 -0.985159957 -0.6394443197 -0.389657019 -1.4772204077
## 1453  0.081387134  2.009806578 -0.0552000534 -1.174467869 -0.6169262975
## 1454 -0.191140729  0.760747843 -1.5071690913  0.240486118 -0.7890388822
## 1455 -0.317048006  1.620780822 -0.0062670552  0.782766719  1.3884204407
## 1456 -0.621595124  0.464830106  0.0174916580 -0.848629437 -0.0291864731
## 1457  0.333062697 -0.503390924  1.0970405596  0.465082392 -0.2054268299
## 1458 -0.447836979  0.330576263  0.0285286543 -0.814616048 -0.0463616270
## 1459 -0.490040292 -0.157186497 -0.5917799674 -1.167185762 -0.1537424921
## 1460 -0.789663284 -0.194750796  0.7209362379  0.384404110  1.3557950095
## 1461 -0.729739877  0.108420797 -0.3706488993  3.538777915  0.9884322841
## 1462  0.404976050  1.083014074  1.3118651629  2.262386882  1.3342585747
## 1463  1.865987905 -1.866527036 -1.5282088616  1.600847174 -0.3606740275
## 1464  0.389452105 -0.757228139  1.4234180344 -0.004402066 -0.7714978440
## 1465 -0.723267174 -1.051409469  0.1125859930 -0.488644290  0.8822654175
## 1466 -0.537973485 -0.199149211 -0.6176020137  0.905185783  0.4383741597
## 1467  0.288063247 -0.162302425  1.2624871110 -0.211934095  1.6646342030
## 1468 -0.363648244 -0.644445192  0.7699614858 -0.413237143 -0.7820553802
## 1469  0.392994518  0.371654956 -0.3461808265 -0.121991477  1.2095418303
## 1470 -0.413010977 -0.340161244  1.0000164249 -0.793819984 -0.8079035956

#Clustering
# Kmeans optimal clusters
# As we have two factors, Yes and No in Attrition, we check the clustering for 2 clusters only.

set.seed(42)
matstd_attr <- scale(efa_data)

km.res <- kmeans(matstd_attr, 2, nstart = 10)

fviz_cluster(km.res, data = matstd_attr,
             ellipse.type = "convex",
             palette = "jco",
             ggtheme = theme_minimal())

# We have used the efa_data for the clustering of the forst approach.
# We can check the precision and recall using the confusion matrix below.


Clustered <- ifelse(km.res$cluster > 1, "Attrited", "Not Attrited")
Actual <- ifelse(attr$Attrition == 1, "Attrited", "Not Attrited")
confusion_mat <- table(Clustered, Actual)
confusion_mat

##               Actual
## Clustered      Not Attrited
##   Attrited              903
##   Not Attrited          567

accuracy <- sum(diag(confusion_mat)) / sum(confusion_mat)
precision <- confusion_mat[1, 1] / sum(confusion_mat[, 1])
recall <- confusion_mat[1, 1] / sum(confusion_mat[1, ])
cat("Accuracy:", round(accuracy, 3), "\n")

## Accuracy: 0.614

cat("Precision:", round(precision, 3), "\n")

## Precision: 0.614

cat("Recall:", round(recall, 3), "\n")

## Recall: 1

# Although we have a recall of 1, we can see that the confusion matrix shows the clustering is done in a way where almost all the employees are on the same side.
# This shows that we cannot classify our data into Yes and No in Attrition based on the variables given.
# We can now check the clustering using the second approach.

#New Data
set.seed(42)
matstd_attr1 <- scale(pca_data)

km.res1 <- kmeans(matstd_attr1, 2, nstart = 10)

fviz_cluster(km.res1, data = matstd_attr1,
             ellipse.type = "convex",
             palette = "jco",
             ggtheme = theme_minimal())

# We have used the pca_data for the clustering of the forst approach.
# We can check the precision and recall using the confusion matrix below.

Clustered1 <- ifelse(km.res$cluster > 1, "Attrited", "Not Attrited")
Actual <- ifelse(attr$Attrition == 1, "Attrited", "Not Attrited")
confusion_mat1 <- table(Clustered1, Actual)
confusion_mat1

##               Actual
## Clustered1     Not Attrited
##   Attrited              903
##   Not Attrited          567

accuracy1 <- sum(diag(confusion_mat1)) / sum(confusion_mat1)
precision1 <- confusion_mat1[1, 1] / sum(confusion_mat1[, 1])
recall1 <- confusion_mat1[1, 1] / sum(confusion_mat1[1, ])
cat("Accuracy:", round(accuracy1, 3), "\n")

## Accuracy: 0.614

cat("Precision:", round(precision1, 3), "\n")

## Precision: 0.614

cat("Recall:", round(recall1, 3), "\n")

## Recall: 1

#The precision is obtained to be 39% which is not so good.

#Regression & Logistic Regression

attrition_data <- read.csv("/Users/meet/Desktop/Attrition Data copy.csv",row.names=1, fill = TRUE)
attrition_data

##                  Department MaritalStatus   EducationField Attrition Education
## 1                     Sales        Single    Life Sciences       Yes         2
## 2    Research & Development       Married    Life Sciences        No         1
## 3    Research & Development        Single            Other       Yes         2
## 4    Research & Development       Married    Life Sciences        No         4
## 5    Research & Development       Married          Medical        No         1
## 6    Research & Development        Single    Life Sciences        No         2
## 7    Research & Development       Married          Medical        No         3
## 8    Research & Development      Divorced    Life Sciences        No         1
## 9    Research & Development        Single    Life Sciences        No         3
## 10   Research & Development       Married          Medical        No         3
## 11   Research & Development       Married          Medical        No         3
## 12   Research & Development        Single    Life Sciences        No         2
## 13   Research & Development      Divorced    Life Sciences        No         1
## 14   Research & Development      Divorced          Medical        No         2
## 15   Research & Development        Single    Life Sciences       Yes         3
## 16   Research & Development      Divorced    Life Sciences        No         4
## 17   Research & Development      Divorced    Life Sciences        No         2
## 18   Research & Development      Divorced          Medical        No         2
## 19                    Sales       Married    Life Sciences        No         4
## 20   Research & Development        Single    Life Sciences        No         3
## 21   Research & Development      Divorced            Other        No         2
## 22                    Sales        Single    Life Sciences       Yes         4
## 23   Research & Development        Single    Life Sciences        No         4
## 24   Research & Development        Single    Life Sciences        No         2
## 25   Research & Development        Single          Medical       Yes         1
## 26   Research & Development      Divorced            Other        No         3
## 27   Research & Development        Single    Life Sciences       Yes         1
## 28                    Sales       Married        Marketing        No         4
## 29   Research & Development       Married          Medical        No         4
## 30                    Sales        Single        Marketing        No         4
## 31   Research & Development        Single          Medical        No         3
## 32   Research & Development       Married            Other        No         4
## 33   Research & Development        Single          Medical        No         2
## 34                    Sales       Married Technical Degree       Yes         3
## 35   Research & Development       Married          Medical       Yes         3
## 36   Research & Development      Divorced          Medical        No         2
## 37                    Sales       Married        Marketing       Yes         2
## 38                    Sales       Married        Marketing        No         3
## 39   Research & Development       Married    Life Sciences        No         4
## 40                    Sales       Married    Life Sciences        No         3
## 41   Research & Development      Divorced            Other        No         2
## 42   Research & Development      Divorced    Life Sciences        No         4
## 43   Research & Development        Single    Life Sciences       Yes         3
## 44                    Sales        Single    Life Sciences        No         3
## 45   Research & Development        Single          Medical        No         2
## 46   Research & Development       Married Technical Degree       Yes         3
## 47                    Sales        Single        Marketing        No         4
## 48   Research & Development       Married    Life Sciences        No         2
## 49                    Sales        Single        Marketing        No         4
## 50   Research & Development       Married    Life Sciences        No         1
## 51   Research & Development        Single    Life Sciences       Yes         2
## 52   Research & Development        Single Technical Degree       Yes         4
## 53                    Sales      Divorced        Marketing        No         5
## 54   Research & Development       Married          Medical        No         2
## 55                    Sales       Married        Marketing        No         3
## 56   Research & Development        Single    Life Sciences        No         2
## 57                    Sales       Married    Life Sciences        No         5
## 58   Research & Development       Married          Medical        No         4
## 59   Research & Development      Divorced    Life Sciences        No         4
## 60   Research & Development      Divorced    Life Sciences        No         4
## 61   Research & Development       Married          Medical        No         3
## 62   Research & Development        Single    Life Sciences        No         5
## 63   Research & Development      Divorced          Medical        No         2
## 64                    Sales        Single    Life Sciences        No         3
## 65   Research & Development      Divorced Technical Degree        No         3
## 66   Research & Development      Divorced          Medical        No         3
## 67   Research & Development        Single    Life Sciences        No         3
## 68   Research & Development      Divorced    Life Sciences        No         3
## 69   Research & Development       Married          Medical        No         3
## 70   Research & Development       Married          Medical       Yes         3
## 71                    Sales        Single    Life Sciences        No         1
## 72   Research & Development       Married    Life Sciences        No         3
## 73   Research & Development        Single          Medical        No         4
## 74   Research & Development       Married    Life Sciences        No         3
## 75   Research & Development       Married    Life Sciences        No         3
## 76   Research & Development        Single    Life Sciences        No         4
## 77                    Sales        Single        Marketing        No         4
## 78   Research & Development       Married            Other        No         4
## 79   Research & Development        Single          Medical        No         4
## 80          Human Resources      Divorced          Medical        No         2
## 81   Research & Development       Married    Life Sciences        No         1
## 82   Research & Development        Single          Medical        No         3
## 83                    Sales       Married    Life Sciences        No         2
## 84   Research & Development      Divorced          Medical        No         3
## 85   Research & Development       Married          Medical        No         2
## 86   Research & Development        Single    Life Sciences        No         3
## 87                    Sales      Divorced Technical Degree        No         1
## 88   Research & Development       Married    Life Sciences        No         4
## 89   Research & Development       Married    Life Sciences        No         3
## 90                    Sales        Single          Medical       Yes         2
## 91   Research & Development       Married    Life Sciences        No         4
## 92                    Sales        Single        Marketing        No         4
## 93                    Sales      Divorced          Medical        No         2
## 94   Research & Development       Married          Medical        No         3
## 95                    Sales        Single          Medical        No         4
## 96   Research & Development       Married Technical Degree        No         4
## 97                    Sales       Married            Other        No         2
## 98                    Sales       Married          Medical        No         3
## 99                    Sales        Single          Medical        No         4
## 100  Research & Development       Married          Medical        No         3
## 101         Human Resources      Divorced  Human Resources       Yes         4
## 102  Research & Development        Single    Life Sciences        No         1
## 103  Research & Development        Single    Life Sciences       Yes         3
## 104  Research & Development        Single            Other        No         4
## 105  Research & Development      Divorced    Life Sciences        No         2
## 106         Human Resources       Married  Human Resources        No         4
## 107  Research & Development       Married    Life Sciences        No         3
## 108                   Sales        Single        Marketing       Yes         3
## 109  Research & Development       Married          Medical        No         1
## 110  Research & Development        Single          Medical        No         3
## 111  Research & Development        Single          Medical        No         4
## 112  Research & Development        Single    Life Sciences       Yes         3
## 113         Human Resources        Single  Human Resources        No         3
## 114  Research & Development       Married    Life Sciences        No         1
## 115  Research & Development      Divorced    Life Sciences        No         4
## 116                   Sales        Single    Life Sciences        No         3
## 117  Research & Development        Single          Medical        No         3
## 118                   Sales       Married Technical Degree        No         2
## 119  Research & Development      Divorced    Life Sciences        No         2
## 120                   Sales       Married    Life Sciences        No         2
## 121  Research & Development      Divorced    Life Sciences        No         3
## 122                   Sales       Married        Marketing        No         2
## 123  Research & Development       Married    Life Sciences       Yes         4
## 124  Research & Development        Single    Life Sciences        No         3
## 125                   Sales       Married    Life Sciences       Yes         4
## 126  Research & Development       Married            Other        No         3
## 127  Research & Development       Married          Medical       Yes         4
## 128                   Sales        Single        Marketing       Yes         1
## 129  Research & Development       Married Technical Degree        No         1
## 130  Research & Development       Married          Medical        No         4
## 131  Research & Development        Single          Medical        No         3
## 132                   Sales        Single        Marketing        No         3
## 133                   Sales       Married    Life Sciences       Yes         3
## 134                   Sales      Divorced    Life Sciences        No         1
## 135         Human Resources       Married    Life Sciences        No         1
## 136  Research & Development      Divorced          Medical        No         2
## 137  Research & Development        Single    Life Sciences       Yes         4
## 138                   Sales       Married    Life Sciences        No         4
## 139                   Sales       Married    Life Sciences        No         3
## 140         Human Resources       Married  Human Resources        No         3
## 141  Research & Development        Single          Medical       Yes         3
## 142  Research & Development        Single          Medical        No         3
## 143  Research & Development        Single Technical Degree        No         5
## 144  Research & Development        Single    Life Sciences        No         3
## 145                   Sales      Divorced          Medical        No         2
## 146  Research & Development      Divorced Technical Degree        No         3
## 147  Research & Development        Single          Medical        No         1
## 148  Research & Development      Divorced    Life Sciences        No         3
## 149  Research & Development       Married    Life Sciences        No         4
## 150  Research & Development        Single          Medical        No         1
## 151  Research & Development      Divorced          Medical        No         3
## 152                   Sales       Married        Marketing        No         5
## 153                   Sales       Married        Marketing        No         2
## 154  Research & Development      Divorced    Life Sciences        No         3
## 155                   Sales        Single        Marketing        No         3
## 156  Research & Development       Married Technical Degree        No         1
## 157  Research & Development       Married          Medical        No         4
## 158  Research & Development       Married          Medical        No         3
## 159                   Sales       Married        Marketing        No         4
## 160                   Sales       Married        Marketing        No         4
## 161  Research & Development       Married          Medical        No         1
## 162  Research & Development      Divorced          Medical        No         3
## 163  Research & Development       Married          Medical        No         3
## 164  Research & Development      Divorced    Life Sciences        No         2
## 165  Research & Development      Divorced          Medical        No         3
## 166  Research & Development        Single    Life Sciences        No         3
## 167  Research & Development      Divorced    Life Sciences        No         3
## 168                   Sales       Married    Life Sciences        No         3
## 169                   Sales        Single    Life Sciences        No         4
## 170  Research & Development        Single    Life Sciences        No         5
## 171  Research & Development       Married Technical Degree        No         3
## 172                   Sales        Single Technical Degree       Yes         1
## 173  Research & Development        Single          Medical        No         2
## 174  Research & Development      Divorced          Medical        No         3
## 175                   Sales      Divorced    Life Sciences        No         2
## 176  Research & Development      Divorced    Life Sciences        No         3
## 177  Research & Development        Single    Life Sciences        No         3
## 178  Research & Development        Single    Life Sciences       Yes         3
## 179                   Sales      Divorced        Marketing        No         2
## 180  Research & Development        Single    Life Sciences        No         2
## 181  Research & Development       Married          Medical        No         1
## 182  Research & Development        Single          Medical        No         2
## 183                   Sales        Single        Marketing       Yes         2
## 184  Research & Development       Married          Medical        No         3
## 185  Research & Development      Divorced          Medical        No         2
## 186  Research & Development       Married          Medical        No         3
## 187  Research & Development       Married          Medical        No         1
## 188  Research & Development        Single          Medical        No         4
## 189  Research & Development       Married    Life Sciences        No         1
## 190  Research & Development        Single          Medical        No         3
## 191  Research & Development       Married    Life Sciences        No         4
## 192  Research & Development        Single          Medical        No         3
## 193  Research & Development       Married    Life Sciences       Yes         2
## 194  Research & Development      Divorced          Medical        No         3
## 195  Research & Development       Married          Medical        No         2
## 196  Research & Development       Married    Life Sciences        No         3
## 197  Research & Development        Single          Medical        No         3
## 198  Research & Development      Divorced          Medical        No         2
## 199  Research & Development       Married    Life Sciences        No         4
## 200  Research & Development       Married Technical Degree        No         3
## 201  Research & Development       Married Technical Degree        No         1
## 202  Research & Development      Divorced    Life Sciences        No         4
## 203  Research & Development      Divorced          Medical        No         4
## 204  Research & Development       Married          Medical        No         2
## 205  Research & Development       Married          Medical       Yes         1
## 206                   Sales       Married        Marketing       Yes         3
## 207  Research & Development      Divorced    Life Sciences        No         3
## 208  Research & Development        Single          Medical        No         1
## 209  Research & Development       Married    Life Sciences        No         5
## 210  Research & Development      Divorced          Medical        No         4
## 211                   Sales       Married          Medical       Yes         4
## 212  Research & Development        Single    Life Sciences        No         1
## 213                   Sales        Single    Life Sciences        No         3
## 214  Research & Development       Married    Life Sciences        No         4
## 215  Research & Development        Single Technical Degree       Yes         3
## 216                   Sales        Single    Life Sciences        No         3
## 217                   Sales        Single        Marketing       Yes         4
## 218  Research & Development        Single Technical Degree       Yes         3
## 219                   Sales        Single          Medical        No         3
## 220                   Sales       Married        Marketing        No         3
## 221  Research & Development        Single    Life Sciences        No         2
## 222  Research & Development       Married          Medical        No         4
## 223  Research & Development      Divorced            Other        No         3
## 224                   Sales      Divorced    Life Sciences        No         3
## 225  Research & Development       Married          Medical        No         4
## 226  Research & Development       Married    Life Sciences        No         3
## 227                   Sales      Divorced        Marketing        No         4
## 228                   Sales       Married          Medical        No         1
## 229                   Sales        Single        Marketing        No         3
## 230  Research & Development        Single          Medical       Yes         1
## 231  Research & Development        Single    Life Sciences        No         3
## 232  Research & Development       Married Technical Degree        No         2
## 233         Human Resources       Married          Medical        No         2
## 234                   Sales      Divorced          Medical        No         4
## 235  Research & Development       Married          Medical       Yes         3
## 236                   Sales       Married        Marketing        No         3
## 237  Research & Development       Married    Life Sciences       Yes         2
## 238                   Sales        Single    Life Sciences        No         4
## 239                   Sales       Married    Life Sciences        No         2
## 240  Research & Development        Single    Life Sciences       Yes         3
## 241  Research & Development      Divorced          Medical        No         4
## 242                   Sales       Married        Marketing        No         4
## 243  Research & Development      Divorced    Life Sciences        No         2
## 244  Research & Development      Divorced Technical Degree        No         2
## 245  Research & Development       Married            Other        No         3
## 246  Research & Development      Divorced          Medical        No         4
## 247  Research & Development       Married    Life Sciences        No         4
## 248  Research & Development       Married    Life Sciences        No         4
## 249  Research & Development       Married          Medical        No         2
## 250  Research & Development       Married    Life Sciences        No         4
## 251  Research & Development      Divorced          Medical       Yes         3
## 252  Research & Development        Single Technical Degree        No         4
## 253  Research & Development        Single    Life Sciences        No         3
## 254  Research & Development        Single    Life Sciences        No         2
## 255                   Sales      Divorced        Marketing        No         2
## 256  Research & Development       Married    Life Sciences        No         3
## 257  Research & Development      Divorced          Medical        No         3
## 258  Research & Development      Divorced          Medical        No         2
## 259  Research & Development       Married    Life Sciences        No         3
## 260  Research & Development        Single          Medical       Yes         2
## 261  Research & Development       Married    Life Sciences        No         3
## 262                   Sales       Married    Life Sciences        No         2
## 263  Research & Development        Single Technical Degree        No         1
## 264                   Sales       Married Technical Degree        No         3
## 265  Research & Development        Single    Life Sciences       Yes         4
## 266                   Sales       Married          Medical        No         3
## 267  Research & Development       Married          Medical        No         3
## 268  Research & Development      Divorced    Life Sciences        No         2
## 269  Research & Development       Married          Medical        No         2
## 270  Research & Development       Married    Life Sciences        No         3
## 271  Research & Development        Single          Medical        No         3
## 272  Research & Development       Married    Life Sciences       Yes         4
## 273  Research & Development       Married          Medical        No         3
## 274                   Sales       Married          Medical        No         4
## 275  Research & Development        Single          Medical        No         2
## 276  Research & Development      Divorced          Medical        No         4
## 277  Research & Development      Divorced    Life Sciences        No         3
## 278                   Sales      Divorced          Medical        No         2
## 279  Research & Development      Divorced    Life Sciences        No         3
## 280  Research & Development      Divorced    Life Sciences        No         1
## 281  Research & Development       Married          Medical        No         4
## 282                   Sales       Married    Life Sciences        No         1
## 283                   Sales        Single    Life Sciences        No         2
## 284  Research & Development       Married Technical Degree        No         2
## 285  Research & Development       Married          Medical        No         2
## 286  Research & Development        Single    Life Sciences        No         3
## 287  Research & Development      Divorced    Life Sciences       Yes         3
## 288  Research & Development      Divorced    Life Sciences        No         4
## 289  Research & Development      Divorced          Medical       Yes         4
## 290  Research & Development        Single    Life Sciences        No         2
## 291  Research & Development        Single    Life Sciences        No         4
## 292  Research & Development        Single Technical Degree        No         3
## 293                   Sales      Divorced        Marketing        No         3
## 294                   Sales        Single        Marketing       Yes         4
## 295  Research & Development       Married          Medical        No         3
## 296                   Sales       Married        Marketing        No         3
## 297  Research & Development        Single    Life Sciences       Yes         3
## 298                   Sales       Married        Marketing        No         3
## 299  Research & Development       Married    Life Sciences        No         4
## 300  Research & Development      Divorced          Medical        No         3
## 301                   Sales        Single    Life Sciences        No         4
## 302                   Sales        Single          Medical        No         3
## 303  Research & Development        Single          Medical        No         2
## 304                   Sales       Married Technical Degree        No         3
## 305  Research & Development      Divorced          Medical        No         3
## 306  Research & Development       Married    Life Sciences        No         4
## 307                   Sales       Married    Life Sciences        No         3
## 308  Research & Development       Married    Life Sciences        No         2
## 309  Research & Development      Divorced    Life Sciences        No         4
## 310  Research & Development       Married Technical Degree        No         4
## 311         Human Resources       Married  Human Resources        No         3
## 312  Research & Development      Divorced    Life Sciences        No         3
## 313  Research & Development      Divorced    Life Sciences        No         4
## 314  Research & Development       Married    Life Sciences        No         4
## 315  Research & Development       Married          Medical        No         1
## 316  Research & Development        Single    Life Sciences        No         4
## 317  Research & Development        Single Technical Degree        No         2
## 318  Research & Development       Married          Medical       Yes         4
## 319  Research & Development        Single    Life Sciences        No         3
## 320                   Sales       Married Technical Degree        No         2
## 321                   Sales        Single    Life Sciences        No         3
## 322                   Sales      Divorced        Marketing        No         3
## 323  Research & Development        Single          Medical        No         4
## 324  Research & Development       Married          Medical       Yes         4
## 325  Research & Development       Married          Medical        No         2
## 326  Research & Development       Married    Life Sciences        No         2
## 327  Research & Development       Married          Medical        No         2
## 328                   Sales       Married          Medical       Yes         2
## 329                   Sales        Single        Marketing        No         3
## 330  Research & Development       Married    Life Sciences        No         5
## 331  Research & Development      Divorced    Life Sciences        No         4
## 332                   Sales       Married        Marketing        No         1
## 333  Research & Development        Single    Life Sciences        No         4
## 334  Research & Development       Married    Life Sciences        No         3
## 335  Research & Development       Married            Other        No         4
## 336                   Sales       Married          Medical        No         2
## 337  Research & Development       Married            Other       Yes         4
## 338  Research & Development        Single            Other        No         5
## 339                   Sales      Divorced        Marketing        No         3
## 340                   Sales       Married        Marketing        No         4
## 341  Research & Development      Divorced          Medical        No         2
## 342  Research & Development      Divorced    Life Sciences        No         2
## 343  Research & Development        Single          Medical        No         4
## 344                   Sales      Divorced        Marketing        No         1
## 345  Research & Development        Single Technical Degree        No         4
## 346  Research & Development      Divorced    Life Sciences        No         1
## 347  Research & Development        Single          Medical        No         3
## 348                   Sales        Single          Medical        No         1
## 349  Research & Development        Single    Life Sciences        No         5
## 350                   Sales       Married    Life Sciences        No         3
## 351         Human Resources      Divorced Technical Degree        No         1
## 352  Research & Development       Married          Medical        No         3
## 353                   Sales       Married          Medical        No         1
## 354  Research & Development      Divorced          Medical        No         3
## 355                   Sales       Married Technical Degree        No         2
## 356                   Sales       Married    Life Sciences        No         3
## 357  Research & Development        Single            Other        No         4
## 358                   Sales        Single Technical Degree       Yes         1
## 359                   Sales        Single          Medical        No         5
## 360                   Sales       Married          Medical        No         4
## 361  Research & Development       Married          Medical        No         4
## 362  Research & Development       Married    Life Sciences        No         4
## 363                   Sales        Single          Medical        No         2
## 364                   Sales        Single        Marketing       Yes         3
## 365  Research & Development       Married          Medical        No         3
## 366  Research & Development       Married          Medical        No         4
## 367                   Sales        Single        Marketing       Yes         3
## 368  Research & Development        Single Technical Degree        No         3
## 369                   Sales       Married        Marketing       Yes         2
## 370  Research & Development        Single    Life Sciences        No         4
## 371                   Sales        Single    Life Sciences       Yes         3
## 372  Research & Development        Single    Life Sciences        No         3
## 373  Research & Development        Single    Life Sciences        No         4
## 374  Research & Development      Divorced          Medical        No         2
## 375                   Sales        Single    Life Sciences        No         4
## 376  Research & Development        Single            Other        No         3
## 377                   Sales       Married    Life Sciences        No         2
## 378  Research & Development       Married    Life Sciences        No         3
## 379                   Sales        Single        Marketing       Yes         3
## 380  Research & Development        Single    Life Sciences        No         3
## 381                   Sales      Divorced        Marketing        No         4
## 382                   Sales       Married Technical Degree        No         1
## 383  Research & Development        Single Technical Degree       Yes         1
## 384  Research & Development       Married          Medical        No         3
## 385                   Sales       Married          Medical        No         2
## 386  Research & Development        Single Technical Degree       Yes         3
## 387  Research & Development      Divorced    Life Sciences        No         3
## 388                   Sales      Divorced        Marketing        No         2
## 389  Research & Development      Divorced    Life Sciences        No         4
## 390  Research & Development        Single    Life Sciences        No         4
## 391  Research & Development      Divorced    Life Sciences        No         3
## 392  Research & Development       Married          Medical        No         3
## 393  Research & Development       Married          Medical        No         2
## 394                   Sales       Married        Marketing        No         4
## 395  Research & Development       Married          Medical        No         2
## 396  Research & Development       Married          Medical        No         3
## 397  Research & Development      Divorced            Other        No         4
## 398                   Sales        Single    Life Sciences        No         2
## 399  Research & Development       Married          Medical        No         5
## 400  Research & Development       Married    Life Sciences        No         2
## 401  Research & Development      Divorced    Life Sciences        No         1
## 402                   Sales       Married    Life Sciences        No         3
## 403                   Sales        Single Technical Degree        No         3
## 404                   Sales       Married        Marketing        No         3
## 405  Research & Development      Divorced          Medical        No         2
## 406  Research & Development       Married          Medical       Yes         3
## 407  Research & Development       Married          Medical        No         3
## 408  Research & Development       Married    Life Sciences        No         2
## 409  Research & Development       Married    Life Sciences        No         2
## 410  Research & Development      Divorced    Life Sciences        No         2
## 411  Research & Development        Single    Life Sciences        No         3
## 412  Research & Development       Married    Life Sciences        No         3
## 413  Research & Development      Divorced          Medical        No         3
## 414  Research & Development       Married Technical Degree        No         4
## 415                   Sales        Single Technical Degree       Yes         1
## 416                   Sales      Divorced        Marketing       Yes         2
## 417  Research & Development       Married    Life Sciences        No         2
## 418                   Sales       Married    Life Sciences        No         4
## 419  Research & Development      Divorced    Life Sciences        No         3
## 420  Research & Development       Married    Life Sciences        No         3
## 421  Research & Development       Married          Medical        No         4
## 422  Research & Development       Married Technical Degree       Yes         5
## 423         Human Resources        Single Technical Degree       Yes         2
## 424                   Sales       Married            Other        No         4
## 425                   Sales      Divorced        Marketing        No         3
## 426  Research & Development       Married    Life Sciences        No         4
## 427  Research & Development        Single          Medical        No         3
## 428                   Sales       Married        Marketing        No         3
## 429  Research & Development      Divorced          Medical        No         2
## 430  Research & Development       Married    Life Sciences        No         3
## 431  Research & Development        Single    Life Sciences        No         3
## 432  Research & Development        Single    Life Sciences        No         4
## 433  Research & Development      Divorced    Life Sciences        No         4
## 434                   Sales       Married        Marketing        No         3
## 435  Research & Development      Divorced    Life Sciences        No         1
## 436  Research & Development       Married          Medical       Yes         1
## 437  Research & Development      Divorced          Medical       Yes         1
## 438                   Sales        Single        Marketing        No         1
## 439  Research & Development       Married    Life Sciences        No         3
## 440  Research & Development       Married    Life Sciences       Yes         3
## 441         Human Resources      Divorced  Human Resources       Yes         3
## 442  Research & Development       Married            Other        No         2
## 443                   Sales        Single          Medical        No         4
## 444  Research & Development        Single Technical Degree       Yes         1
## 445                   Sales       Married        Marketing        No         5
## 446                   Sales        Single    Life Sciences        No         5
## 447                   Sales        Single    Life Sciences        No         2
## 448                   Sales       Married        Marketing        No         3
## 449  Research & Development        Single    Life Sciences        No         3
## 450  Research & Development       Married    Life Sciences        No         1
## 451                   Sales        Single    Life Sciences        No         1
## 452  Research & Development       Married          Medical        No         3
## 453                   Sales       Married            Other        No         3
## 454         Human Resources      Divorced    Life Sciences       Yes         4
## 455  Research & Development      Divorced Technical Degree        No         3
## 456  Research & Development      Divorced          Medical        No         5
## 457                   Sales      Divorced    Life Sciences        No         3
## 458                   Sales        Single        Marketing       Yes         3
## 459                   Sales      Divorced            Other        No         3
## 460  Research & Development        Single            Other        No         4
## 461                   Sales      Divorced          Medical        No         2
## 462                   Sales        Single          Medical        No         3
## 463                   Sales        Single    Life Sciences        No         4
## 464  Research & Development        Single Technical Degree       Yes         3
## 465  Research & Development        Single Technical Degree        No         3
## 466  Research & Development       Married          Medical        No         1
## 467                   Sales       Married    Life Sciences        No         5
## 468                   Sales      Divorced          Medical        No         4
## 469  Research & Development      Divorced Technical Degree        No         2
## 470                   Sales       Married            Other       Yes         4
## 471                   Sales       Married          Medical        No         3
## 472  Research & Development       Married          Medical        No         3
## 473  Research & Development       Married    Life Sciences        No         4
## 474  Research & Development      Divorced    Life Sciences        No         4
## 475  Research & Development       Married          Medical        No         3
## 476                   Sales       Married        Marketing        No         2
## 477  Research & Development       Married            Other        No         2
## 478         Human Resources       Married          Medical        No         3
## 479                   Sales       Married          Medical        No         1
## 480  Research & Development       Married    Life Sciences       Yes         3
## 481                   Sales       Married    Life Sciences       Yes         4
## 482  Research & Development       Married    Life Sciences        No         2
## 483                   Sales      Divorced          Medical       Yes         4
## 484  Research & Development        Single            Other        No         2
## 485                   Sales      Divorced          Medical        No         4
## 486  Research & Development      Divorced          Medical        No         4
## 487                   Sales       Married        Marketing        No         3
## 488  Research & Development        Single    Life Sciences        No         3
## 489  Research & Development       Married    Life Sciences        No         4
## 490  Research & Development      Divorced            Other        No         4
## 491  Research & Development        Single    Life Sciences        No         1
## 492  Research & Development      Divorced          Medical        No         5
## 493  Research & Development       Married    Life Sciences        No         4
## 494         Human Resources        Single    Life Sciences        No         4
## 495                   Sales      Divorced Technical Degree        No         3
## 496                   Sales      Divorced        Marketing       Yes         1
## 497                   Sales        Single Technical Degree        No         1
## 498  Research & Development       Married            Other        No         4
## 499  Research & Development       Married          Medical        No         1
## 500                   Sales      Divorced        Marketing        No         4
## 501  Research & Development       Married    Life Sciences        No         4
## 502  Research & Development      Divorced          Medical        No         3
## 503                   Sales        Single          Medical        No         1
## 504  Research & Development       Married    Life Sciences        No         5
## 505                   Sales       Married    Life Sciences       Yes         4
## 506  Research & Development       Married    Life Sciences        No         3
## 507  Research & Development       Married            Other        No         3
## 508                   Sales       Married          Medical        No         2
## 509  Research & Development        Single    Life Sciences        No         4
## 510  Research & Development      Divorced    Life Sciences        No         3
## 511         Human Resources       Married          Medical        No         4
## 512  Research & Development      Divorced          Medical        No         2
## 513  Research & Development        Single          Medical        No         4
## 514  Research & Development        Single          Medical       Yes         1
## 515  Research & Development        Single    Life Sciences       Yes         3
## 516  Research & Development       Married    Life Sciences        No         3
## 517  Research & Development       Married          Medical        No         3
## 518                   Sales       Married    Life Sciences        No         3
## 519                   Sales        Single        Marketing        No         4
## 520  Research & Development      Divorced    Life Sciences        No         4
## 521                   Sales       Married        Marketing        No         1
## 522                   Sales      Divorced          Medical        No         1
## 523  Research & Development        Single    Life Sciences        No         2
## 524  Research & Development       Married          Medical        No         1
## 525  Research & Development        Single          Medical        No         3
## 526                   Sales        Single    Life Sciences       Yes         2
## 527  Research & Development        Single Technical Degree        No         4
## 528                   Sales        Single        Marketing        No         3
## 529                   Sales       Married Technical Degree       Yes         2
## 530  Research & Development        Single    Life Sciences        No         4
## 531  Research & Development       Married    Life Sciences        No         2
## 532  Research & Development        Single    Life Sciences        No         2
## 533                   Sales        Single        Marketing        No         4
## 534                   Sales       Married    Life Sciences        No         4
## 535  Research & Development       Married    Life Sciences        No         3
## 536         Human Resources      Divorced  Human Resources        No         4
## 537                   Sales        Single        Marketing        No         4
## 538  Research & Development      Divorced    Life Sciences        No         2
## 539         Human Resources       Married  Human Resources        No         3
## 540                   Sales       Married        Marketing        No         4
## 541  Research & Development        Single    Life Sciences       Yes         2
## 542  Research & Development       Married    Life Sciences        No         3
## 543  Research & Development        Single    Life Sciences        No         3
## 544  Research & Development        Single          Medical        No         3
## 545                   Sales      Divorced          Medical        No         3
## 546                   Sales      Divorced        Marketing        No         5
## 547                   Sales        Single    Life Sciences        No         3
## 548  Research & Development      Divorced          Medical       Yes         3
## 549                   Sales       Married    Life Sciences        No         3
## 550  Research & Development        Single          Medical        No         2
## 551  Research & Development       Married          Medical        No         1
## 552         Human Resources       Married  Human Resources        No         3
## 553  Research & Development       Married          Medical        No         3
## 554  Research & Development        Single          Medical        No         1
## 555  Research & Development        Single          Medical        No         3
## 556                   Sales      Divorced        Marketing        No         3
## 557  Research & Development        Single    Life Sciences        No         3
## 558  Research & Development      Divorced    Life Sciences        No         4
## 559  Research & Development       Married    Life Sciences        No         4
## 560  Research & Development       Married          Medical        No         5
## 561  Research & Development      Divorced    Life Sciences        No         5
## 562                   Sales       Married        Marketing        No         4
## 563  Research & Development        Single            Other       Yes         4
## 564                   Sales        Single          Medical        No         1
## 565                   Sales        Single Technical Degree        No         2
## 566  Research & Development        Single          Medical        No         1
## 567                   Sales        Single    Life Sciences       Yes         2
## 568                   Sales        Single            Other        No         3
## 569  Research & Development       Married          Medical       Yes         3
## 570                   Sales        Single    Life Sciences        No         4
## 571  Research & Development       Married          Medical        No         4
## 572  Research & Development      Divorced    Life Sciences        No         2
## 573  Research & Development       Married          Medical        No         3
## 574                   Sales        Single Technical Degree       Yes         3
## 575  Research & Development        Single    Life Sciences        No         4
## 576  Research & Development      Divorced          Medical        No         4
## 577                   Sales       Married        Marketing        No         1
## 578  Research & Development      Divorced    Life Sciences        No         1
## 579  Research & Development        Single    Life Sciences        No         4
## 580  Research & Development        Single          Medical        No         4
## 581                   Sales       Married    Life Sciences        No         4
## 582  Research & Development       Married    Life Sciences        No         3
## 583  Research & Development       Married          Medical        No         2
## 584                   Sales       Married    Life Sciences        No         2
## 585  Research & Development      Divorced    Life Sciences        No         3
## 586  Research & Development       Married    Life Sciences       Yes         3
## 587  Research & Development      Divorced    Life Sciences        No         3
## 588  Research & Development       Married    Life Sciences        No         4
## 589  Research & Development       Married          Medical        No         3
## 590  Research & Development       Married    Life Sciences       Yes         2
## 591  Research & Development       Married          Medical        No         3
## 592                   Sales        Single        Marketing       Yes         3
## 593  Research & Development       Married            Other        No         2
## 594  Research & Development       Married            Other        No         3
## 595  Research & Development       Married    Life Sciences        No         2
## 596  Research & Development        Single    Life Sciences       Yes         4
## 597  Research & Development        Single    Life Sciences        No         4
## 598  Research & Development       Married    Life Sciences        No         2
## 599  Research & Development        Single          Medical       Yes         4
## 600         Human Resources       Married  Human Resources        No         3
## 601  Research & Development       Married    Life Sciences        No         3
## 602  Research & Development        Single          Medical        No         4
## 603  Research & Development        Single          Medical        No         3
## 604  Research & Development        Single    Life Sciences        No         3
## 605  Research & Development       Married    Life Sciences        No         3
## 606  Research & Development      Divorced    Life Sciences        No         3
## 607  Research & Development        Single    Life Sciences        No         4
## 608                   Sales       Married        Marketing       Yes         3
## 609                   Sales        Single          Medical       Yes         1
## 610  Research & Development       Married    Life Sciences        No         2
## 611  Research & Development      Divorced Technical Degree        No         1
## 612  Research & Development        Single            Other        No         3
## 613                   Sales       Married        Marketing        No         4
## 614         Human Resources       Married  Human Resources        No         2
## 615  Research & Development       Married          Medical       Yes         2
## 616  Research & Development       Married          Medical        No         3
## 617                   Sales       Married        Marketing        No         4
## 618  Research & Development        Single          Medical        No         3
## 619  Research & Development        Single          Medical        No         1
## 620                   Sales      Divorced          Medical        No         3
## 621  Research & Development        Single          Medical        No         1
## 622                   Sales       Married    Life Sciences        No         2
## 623                   Sales      Divorced    Life Sciences        No         4
## 624  Research & Development      Divorced    Life Sciences        No         4
## 625                   Sales       Married        Marketing        No         2
## 626                   Sales      Divorced        Marketing        No         3
## 627  Research & Development       Married          Medical        No         2
## 628  Research & Development       Married          Medical        No         4
## 629                   Sales      Divorced        Marketing        No         4
## 630         Human Resources      Divorced          Medical        No         2
## 631  Research & Development       Married    Life Sciences        No         2
## 632  Research & Development       Married    Life Sciences        No         4
## 633  Research & Development        Single          Medical        No         1
## 634         Human Resources       Married    Life Sciences        No         3
## 635                   Sales       Married            Other        No         1
## 636  Research & Development       Married    Life Sciences        No         3
## 637  Research & Development      Divorced    Life Sciences       Yes         4
## 638  Research & Development      Divorced    Life Sciences        No         3
## 639                   Sales       Married        Marketing        No         1
## 640  Research & Development       Married Technical Degree        No         3
## 641  Research & Development       Married    Life Sciences        No         1
## 642                   Sales       Married    Life Sciences        No         2
## 643                   Sales       Married        Marketing        No         3
## 644  Research & Development       Married    Life Sciences        No         3
## 645  Research & Development       Married    Life Sciences        No         4
## 646                   Sales      Divorced          Medical       Yes         3
## 647                   Sales       Married        Marketing        No         3
## 648  Research & Development       Married Technical Degree        No         3
## 649                   Sales       Married          Medical        No         2
## 650  Research & Development        Single    Life Sciences        No         4
## 651  Research & Development       Married    Life Sciences        No         3
## 652                   Sales       Married        Marketing        No         2
## 653                   Sales        Single          Medical        No         2
## 654  Research & Development      Divorced    Life Sciences        No         4
## 655         Human Resources       Married    Life Sciences        No         3
## 656         Human Resources      Divorced  Human Resources        No         2
## 657  Research & Development        Single    Life Sciences       Yes         4
## 658  Research & Development      Divorced          Medical        No         1
## 659  Research & Development       Married    Life Sciences        No         2
## 660                   Sales        Single          Medical        No         4
## 661  Research & Development      Divorced    Life Sciences       Yes         1
## 662  Research & Development      Divorced    Life Sciences        No         3
## 663                   Sales        Single          Medical       Yes         3
## 664  Research & Development        Single            Other       Yes         1
## 665  Research & Development       Married    Life Sciences        No         1
## 666                   Sales        Single    Life Sciences        No         4
## 667  Research & Development       Married    Life Sciences       Yes         1
## 668  Research & Development      Divorced    Life Sciences       Yes         4
## 669  Research & Development      Divorced          Medical        No         3
## 670  Research & Development       Married          Medical       Yes         3
## 671  Research & Development        Single    Life Sciences        No         3
## 672  Research & Development      Divorced    Life Sciences        No         3
## 673                   Sales        Single          Medical        No         2
## 674  Research & Development        Single            Other        No         4
## 675  Research & Development      Divorced Technical Degree        No         3
## 676                   Sales       Married    Life Sciences        No         4
## 677  Research & Development       Married    Life Sciences        No         1
## 678  Research & Development       Married            Other        No         2
## 679  Research & Development       Married          Medical        No         4
## 680                   Sales       Married        Marketing        No         2
## 681  Research & Development        Single            Other        No         4
## 682  Research & Development       Married Technical Degree        No         3
## 683  Research & Development       Married    Life Sciences        No         3
## 684                   Sales       Married        Marketing       Yes         2
## 685                   Sales      Divorced        Marketing        No         4
## 686                   Sales        Single          Medical        No         3
## 687  Research & Development        Single          Medical        No         3
## 688  Research & Development        Single          Medical        No         4
## 689                   Sales        Single            Other       Yes         3
## 690  Research & Development        Single Technical Degree       Yes         3
## 691  Research & Development       Married          Medical        No         3
## 692  Research & Development      Divorced          Medical        No         4
## 693  Research & Development       Married          Medical        No         4
## 694                   Sales       Married    Life Sciences       Yes         1
## 695  Research & Development        Single    Life Sciences        No         3
## 696                   Sales       Married    Life Sciences       Yes         4
## 697  Research & Development       Married    Life Sciences        No         2
## 698                   Sales       Married Technical Degree        No         3
## 699                   Sales       Married          Medical        No         3
## 700  Research & Development       Married    Life Sciences        No         2
## 701  Research & Development        Single Technical Degree       Yes         3
## 702                   Sales      Divorced          Medical        No         2
## 703                   Sales      Divorced            Other        No         2
## 704                   Sales        Single Technical Degree        No         3
## 705                   Sales      Divorced    Life Sciences        No         4
## 706                   Sales        Single    Life Sciences        No         5
## 707                   Sales        Single    Life Sciences       Yes         3
## 708  Research & Development      Divorced          Medical        No         4
## 709                   Sales      Divorced Technical Degree        No         4
## 710  Research & Development        Single          Medical       Yes         2
## 711                   Sales        Single    Life Sciences        No         3
## 712  Research & Development        Single    Life Sciences       Yes         3
## 713  Research & Development        Single    Life Sciences        No         1
## 714  Research & Development      Divorced          Medical        No         4
## 715  Research & Development      Divorced          Medical        No         2
## 716  Research & Development       Married            Other        No         4
## 717  Research & Development      Divorced          Medical        No         3
## 718  Research & Development       Married Technical Degree        No         4
## 719  Research & Development       Married    Life Sciences        No         2
## 720                   Sales        Single    Life Sciences        No         2
## 721  Research & Development       Married    Life Sciences       Yes         3
## 722  Research & Development       Married    Life Sciences        No         3
## 723  Research & Development       Married          Medical        No         1
## 724  Research & Development      Divorced          Medical        No         2
## 725  Research & Development      Divorced          Medical        No         1
## 726  Research & Development      Divorced            Other       Yes         4
## 727  Research & Development       Married    Life Sciences        No         1
## 728  Research & Development        Single    Life Sciences        No         2
## 729  Research & Development       Married Technical Degree        No         3
## 730  Research & Development      Divorced          Medical        No         4
## 731  Research & Development       Married    Life Sciences        No         2
## 732  Research & Development        Single          Medical       Yes         3
## 733  Research & Development        Single          Medical       Yes         3
## 734  Research & Development       Married          Medical        No         2
## 735  Research & Development       Married    Life Sciences        No         1
## 736  Research & Development        Single    Life Sciences        No         3
## 737  Research & Development        Single    Life Sciences        No         4
## 738  Research & Development        Single          Medical        No         2
## 739  Research & Development       Married    Life Sciences        No         1
## 740  Research & Development       Married    Life Sciences        No         4
## 741  Research & Development      Divorced            Other        No         3
## 742                   Sales       Married        Marketing        No         2
## 743  Research & Development       Married    Life Sciences        No         3
## 744  Research & Development        Single    Life Sciences        No         3
## 745  Research & Development       Married          Medical       Yes         2
## 746  Research & Development       Married          Medical        No         4
## 747  Research & Development      Divorced    Life Sciences        No         1
## 748                   Sales        Single    Life Sciences        No         4
## 749                   Sales        Single          Medical       Yes         2
## 750                   Sales       Married        Marketing       Yes         1
## 751                   Sales       Married          Medical        No         3
## 752                   Sales       Married    Life Sciences        No         3
## 753  Research & Development        Single    Life Sciences       Yes         4
## 754  Research & Development        Single          Medical        No         3
## 755                   Sales        Single    Life Sciences        No         1
## 756                   Sales       Married    Life Sciences        No         2
## 757  Research & Development        Single          Medical        No         4
## 758                   Sales      Divorced        Marketing        No         4
## 759                   Sales       Married Technical Degree        No         2
## 760         Human Resources        Single          Medical        No         4
## 761                   Sales       Married        Marketing        No         3
## 762  Research & Development      Divorced            Other       Yes         3
## 763  Research & Development       Married    Life Sciences       Yes         3
## 764                   Sales       Married    Life Sciences        No         4
## 765                   Sales       Married          Medical        No         1
## 766  Research & Development       Married            Other        No         4
## 767  Research & Development       Married          Medical        No         4
## 768  Research & Development        Single            Other        No         3
## 769                   Sales       Married        Marketing        No         3
## 770  Research & Development      Divorced          Medical        No         1
## 771  Research & Development      Divorced          Medical        No         4
## 772                   Sales       Married    Life Sciences        No         4
## 773  Research & Development       Married          Medical        No         3
## 774  Research & Development        Single          Medical        No         5
## 775  Research & Development        Single          Medical        No         1
## 776                   Sales      Divorced          Medical        No         3
## 777                   Sales        Single        Marketing       Yes         3
## 778  Research & Development        Single    Life Sciences       Yes         3
## 779  Research & Development      Divorced    Life Sciences        No         4
## 780  Research & Development       Married    Life Sciences       Yes         4
## 781  Research & Development        Single Technical Degree       Yes         2
## 782  Research & Development       Married          Medical        No         2
## 783  Research & Development       Married            Other        No         3
## 784  Research & Development       Married Technical Degree        No         2
## 785  Research & Development       Married    Life Sciences        No         1
## 786  Research & Development       Married Technical Degree        No         4
## 787  Research & Development       Married    Life Sciences        No         5
## 788  Research & Development       Married    Life Sciences        No         1
## 789  Research & Development        Single            Other        No         3
## 790         Human Resources       Married          Medical       Yes         2
## 791  Research & Development      Divorced    Life Sciences        No         3
## 792                   Sales        Single Technical Degree       Yes         3
## 793  Research & Development        Single          Medical       Yes         4
## 794  Research & Development      Divorced    Life Sciences        No         2
## 795  Research & Development        Single    Life Sciences        No         1
## 796                   Sales      Divorced    Life Sciences        No         4
## 797  Research & Development       Married Technical Degree       Yes         1
## 798  Research & Development      Divorced          Medical       Yes         3
## 799  Research & Development        Single          Medical       Yes         3
## 800  Research & Development       Married          Medical        No         2
## 801  Research & Development      Divorced          Medical       Yes         3
## 802                   Sales        Single            Other       Yes         4
## 803                   Sales       Married    Life Sciences        No         3
## 804  Research & Development       Married    Life Sciences        No         4
## 805  Research & Development        Single          Medical        No         4
## 806                   Sales       Married    Life Sciences        No         4
## 807  Research & Development        Single    Life Sciences        No         4
## 808                   Sales      Divorced        Marketing        No         4
## 809  Research & Development      Divorced    Life Sciences        No         4
## 810  Research & Development      Divorced          Medical        No         3
## 811                   Sales       Married        Marketing        No         1
## 812                   Sales        Single        Marketing        No         2
## 813  Research & Development       Married    Life Sciences        No         3
## 814  Research & Development      Divorced    Life Sciences       Yes         3
## 815  Research & Development        Single          Medical        No         3
## 816  Research & Development        Single Technical Degree        No         1
## 817  Research & Development        Single    Life Sciences        No         3
## 818  Research & Development        Single    Life Sciences        No         4
## 819                   Sales       Married    Life Sciences        No         3
## 820  Research & Development       Married    Life Sciences        No         1
## 821                   Sales      Divorced        Marketing        No         2
## 822                   Sales       Married Technical Degree        No         4
## 823  Research & Development        Single    Life Sciences        No         2
## 824  Research & Development      Divorced    Life Sciences        No         3
## 825  Research & Development        Single          Medical        No         3
## 826  Research & Development       Married          Medical        No         1
## 827         Human Resources       Married  Human Resources        No         3
## 828  Research & Development      Divorced    Life Sciences        No         3
## 829  Research & Development        Single          Medical       Yes         1
## 830                   Sales        Single        Marketing       Yes         4
## 831  Research & Development       Married    Life Sciences        No         4
## 832  Research & Development       Married          Medical       Yes         3
## 833  Research & Development      Divorced          Medical        No         2
## 834  Research & Development       Married    Life Sciences        No         3
## 835                   Sales       Married    Life Sciences        No         1
## 836         Human Resources        Single Technical Degree        No         4
## 837                   Sales       Married    Life Sciences       Yes         1
## 838  Research & Development        Single          Medical        No         4
## 839                   Sales        Single    Life Sciences       Yes         3
## 840                   Sales        Single        Marketing        No         4
## 841  Research & Development       Married          Medical        No         4
## 842  Research & Development        Single          Medical        No         3
## 843  Research & Development       Married    Life Sciences       Yes         1
## 844  Research & Development       Married          Medical        No         4
## 845                   Sales       Married        Marketing        No         3
## 846  Research & Development       Married          Medical        No         2
## 847  Research & Development      Divorced    Life Sciences        No         3
## 848  Research & Development        Single          Medical        No         3
## 849  Research & Development       Married            Other        No         4
## 850                   Sales        Single        Marketing       Yes         3
## 851                   Sales      Divorced    Life Sciences        No         1
## 852  Research & Development      Divorced Technical Degree        No         4
## 853  Research & Development       Married          Medical        No         1
## 854  Research & Development        Single    Life Sciences        No         2
## 855  Research & Development       Married          Medical        No         3
## 856  Research & Development       Married    Life Sciences        No         3
## 857  Research & Development        Single    Life Sciences        No         3
## 858  Research & Development        Single    Life Sciences       Yes         4
## 859  Research & Development      Divorced          Medical        No         2
## 860  Research & Development       Married    Life Sciences        No         1
## 861  Research & Development       Married    Life Sciences       Yes         4
## 862                   Sales       Married        Marketing        No         3
## 863  Research & Development        Single    Life Sciences        No         3
## 864         Human Resources       Married  Human Resources        No         3
## 865  Research & Development      Divorced    Life Sciences       Yes         2
## 866                   Sales      Divorced    Life Sciences        No         4
## 867                   Sales       Married          Medical        No         4
## 868  Research & Development       Married          Medical        No         3
## 869  Research & Development       Married          Medical        No         4
## 870  Research & Development       Married    Life Sciences        No         2
## 871                   Sales       Married    Life Sciences        No         4
## 872  Research & Development       Married    Life Sciences       Yes         2
## 873                   Sales       Married          Medical        No         3
## 874  Research & Development      Divorced    Life Sciences        No         4
## 875  Research & Development      Divorced    Life Sciences        No         4
## 876  Research & Development        Single            Other        No         4
## 877                   Sales        Single        Marketing        No         3
## 878  Research & Development      Divorced Technical Degree        No         4
## 879         Human Resources       Married          Medical        No         5
## 880                   Sales      Divorced        Marketing        No         4
## 881  Research & Development       Married            Other        No         3
## 882  Research & Development        Single    Life Sciences        No         2
## 883  Research & Development      Divorced Technical Degree        No         3
## 884  Research & Development       Married          Medical        No         3
## 885                   Sales      Divorced Technical Degree        No         3
## 886                   Sales        Single    Life Sciences        No         4
## 887  Research & Development       Married          Medical        No         3
## 888  Research & Development       Married          Medical        No         5
## 889                   Sales       Married        Marketing        No         2
## 890  Research & Development       Married    Life Sciences        No         3
## 891  Research & Development      Divorced    Life Sciences        No         4
## 892  Research & Development       Married    Life Sciences        No         1
## 893  Research & Development        Single          Medical       Yes         3
## 894  Research & Development      Divorced    Life Sciences        No         3
## 895  Research & Development       Married    Life Sciences        No         3
## 896  Research & Development       Married          Medical        No         2
## 897  Research & Development        Single          Medical        No         3
## 898                   Sales        Single    Life Sciences        No         3
## 899  Research & Development       Married    Life Sciences        No         3
## 900  Research & Development       Married          Medical        No         2
## 901  Research & Development       Married Technical Degree        No         3
## 902  Research & Development        Single Technical Degree        No         2
## 903  Research & Development      Divorced    Life Sciences        No         2
## 904  Research & Development      Divorced    Life Sciences        No         3
## 905  Research & Development        Single    Life Sciences        No         3
## 906  Research & Development      Divorced    Life Sciences        No         3
## 907  Research & Development       Married Technical Degree        No         3
## 908                   Sales       Married        Marketing        No         3
## 909                   Sales      Divorced        Marketing        No         5
## 910  Research & Development        Single    Life Sciences        No         3
## 911  Research & Development       Married    Life Sciences        No         2
## 912                   Sales        Single    Life Sciences       Yes         1
## 913  Research & Development        Single    Life Sciences        No         2
## 914                   Sales        Single        Marketing       Yes         3
## 915  Research & Development      Divorced          Medical        No         1
## 916  Research & Development        Single    Life Sciences       Yes         2
## 917                   Sales       Married        Marketing        No         2
## 918                   Sales        Single        Marketing        No         3
## 919                   Sales      Divorced    Life Sciences        No         3
## 920  Research & Development        Single          Medical        No         4
## 921  Research & Development      Divorced          Medical        No         3
## 922  Research & Development        Single          Medical        No         4
## 923  Research & Development      Divorced    Life Sciences        No         2
## 924         Human Resources       Married    Life Sciences        No         3
## 925  Research & Development       Married    Life Sciences        No         1
## 926  Research & Development       Married          Medical        No         4
## 927                   Sales        Single        Marketing        No         4
## 928  Research & Development        Single    Life Sciences        No         4
## 929  Research & Development       Married          Medical       Yes         3
## 930  Research & Development       Married    Life Sciences        No         3
## 931  Research & Development        Single          Medical        No         2
## 932  Research & Development        Single          Medical        No         2
## 933  Research & Development      Divorced Technical Degree       Yes         3
## 934  Research & Development        Single Technical Degree        No         3
## 935  Research & Development        Single          Medical        No         3
## 936                   Sales       Married          Medical        No         3
## 937  Research & Development        Single          Medical        No         3
## 938  Research & Development      Divorced          Medical        No         4
## 939  Research & Development      Divorced    Life Sciences        No         4
## 940  Research & Development       Married    Life Sciences       Yes         2
## 941  Research & Development        Single          Medical       Yes         3
## 942  Research & Development       Married Technical Degree        No         3
## 943  Research & Development       Married Technical Degree        No         4
## 944         Human Resources        Single    Life Sciences        No         2
## 945  Research & Development       Married    Life Sciences        No         3
## 946  Research & Development       Married    Life Sciences        No         3
## 947                   Sales        Single        Marketing       Yes         4
## 948                   Sales        Single    Life Sciences       Yes         3
## 949  Research & Development       Married          Medical        No         4
## 950  Research & Development        Single    Life Sciences        No         2
## 951                   Sales      Divorced    Life Sciences        No         4
## 952                   Sales        Single          Medical        No         2
## 953                   Sales        Single    Life Sciences       Yes         3
## 954  Research & Development       Married    Life Sciences       Yes         3
## 955  Research & Development       Married    Life Sciences        No         1
## 956  Research & Development       Married          Medical        No         2
## 957         Human Resources        Single    Life Sciences        No         4
## 958  Research & Development      Divorced    Life Sciences        No         2
## 959  Research & Development      Divorced    Life Sciences        No         3
## 960  Research & Development        Single    Life Sciences        No         3
## 961                   Sales      Divorced        Marketing        No         3
## 962  Research & Development        Single    Life Sciences        No         4
## 963         Human Resources      Divorced    Life Sciences        No         3
## 964                   Sales      Divorced    Life Sciences        No         2
## 965                   Sales        Single          Medical        No         2
## 966  Research & Development       Married          Medical        No         1
## 967  Research & Development       Married          Medical       Yes         4
## 968  Research & Development       Married    Life Sciences        No         4
## 969                   Sales       Married        Marketing        No         3
## 970  Research & Development        Single    Life Sciences        No         3
## 971                   Sales       Married          Medical        No         3
## 972  Research & Development        Single Technical Degree        No         2
## 973  Research & Development        Single    Life Sciences        No         3
## 974  Research & Development       Married          Medical        No         3
## 975                   Sales        Single    Life Sciences        No         1
## 976                   Sales        Single        Marketing       Yes         4
## 977  Research & Development       Married    Life Sciences        No         3
## 978  Research & Development      Divorced Technical Degree        No         1
## 979  Research & Development      Divorced          Medical        No         1
## 980  Research & Development       Married          Medical        No         3
## 981                   Sales        Single    Life Sciences       Yes         3
## 982                   Sales       Married        Marketing       Yes         4
## 983  Research & Development      Divorced    Life Sciences        No         3
## 984  Research & Development        Single Technical Degree        No         4
## 985                   Sales       Married    Life Sciences        No         3
## 986  Research & Development       Married          Medical       Yes         4
## 987                   Sales       Married    Life Sciences        No         4
## 988                   Sales       Married        Marketing        No         3
## 989  Research & Development      Divorced    Life Sciences        No         3
## 990  Research & Development       Married    Life Sciences        No         1
## 991                   Sales       Married    Life Sciences        No         1
## 992                   Sales       Married        Marketing        No         1
## 993  Research & Development       Married    Life Sciences        No         2
## 994                   Sales       Married    Life Sciences        No         1
## 995  Research & Development       Married          Medical        No         2
## 996  Research & Development        Single          Medical        No         3
## 997                   Sales       Married        Marketing        No         3
## 998  Research & Development        Single    Life Sciences       Yes         4
## 999  Research & Development        Single          Medical        No         1
## 1000        Human Resources       Married  Human Resources        No         3
## 1001 Research & Development       Married            Other        No         4
## 1002 Research & Development        Single          Medical        No         3
## 1003 Research & Development        Single    Life Sciences        No         2
## 1004 Research & Development       Married Technical Degree        No         3
## 1005 Research & Development        Single            Other        No         3
## 1006        Human Resources        Single            Other        No         3
## 1007 Research & Development        Single    Life Sciences       Yes         2
## 1008 Research & Development        Single            Other       Yes         1
## 1009 Research & Development        Single          Medical        No         3
## 1010 Research & Development       Married          Medical        No         3
## 1011 Research & Development      Divorced          Medical        No         4
## 1012                  Sales        Single        Marketing        No         4
## 1013                  Sales        Single    Life Sciences       Yes         4
## 1014                  Sales      Divorced        Marketing        No         4
## 1015 Research & Development        Single    Life Sciences        No         5
## 1016 Research & Development      Divorced            Other        No         4
## 1017 Research & Development        Single    Life Sciences       Yes         3
## 1018 Research & Development       Married    Life Sciences        No         1
## 1019 Research & Development        Single    Life Sciences        No         4
## 1020                  Sales       Married        Marketing        No         4
## 1021 Research & Development       Married Technical Degree        No         3
## 1022                  Sales       Married    Life Sciences       Yes         2
## 1023 Research & Development        Single Technical Degree        No         2
## 1024 Research & Development       Married    Life Sciences        No         2
## 1025 Research & Development       Married          Medical        No         4
## 1026                  Sales       Married          Medical        No         1
## 1027                  Sales       Married        Marketing        No         5
## 1028 Research & Development       Married    Life Sciences        No         3
## 1029 Research & Development       Married          Medical        No         5
## 1030 Research & Development      Divorced            Other        No         4
## 1031                  Sales      Divorced    Life Sciences        No         2
## 1032                  Sales      Divorced        Marketing       Yes         3
## 1033 Research & Development        Single    Life Sciences       Yes         3
## 1034 Research & Development        Single    Life Sciences       Yes         5
## 1035 Research & Development      Divorced          Medical        No         3
## 1036        Human Resources        Single          Medical        No         2
## 1037 Research & Development       Married    Life Sciences       Yes         3
## 1038 Research & Development       Married Technical Degree        No         3
## 1039                  Sales      Divorced        Marketing        No         3
## 1040        Human Resources       Married Technical Degree       Yes         4
## 1041 Research & Development      Divorced          Medical        No         1
## 1042                  Sales        Single          Medical        No         3
## 1043 Research & Development        Single    Life Sciences        No         3
## 1044 Research & Development        Single          Medical        No         3
## 1045 Research & Development       Married Technical Degree        No         4
## 1046 Research & Development      Divorced          Medical        No         3
## 1047 Research & Development        Single    Life Sciences        No         3
## 1048                  Sales       Married          Medical        No         3
## 1049                  Sales        Single            Other        No         3
## 1050                  Sales       Married    Life Sciences        No         1
## 1051 Research & Development        Single          Medical        No         2
## 1052                  Sales       Married        Marketing        No         5
## 1053 Research & Development      Divorced Technical Degree        No         3
## 1054 Research & Development       Married    Life Sciences        No         2
## 1055 Research & Development      Divorced    Life Sciences        No         4
## 1056 Research & Development      Divorced          Medical        No         3
## 1057                  Sales       Married Technical Degree       Yes         3
## 1058                  Sales        Single Technical Degree       Yes         3
## 1059                  Sales        Single          Medical       Yes         4
## 1060                  Sales       Married    Life Sciences        No         1
## 1061 Research & Development        Single          Medical       Yes         3
## 1062                  Sales       Married    Life Sciences        No         2
## 1063 Research & Development        Single          Medical        No         1
## 1064                  Sales      Divorced    Life Sciences        No         3
## 1065        Human Resources      Divorced    Life Sciences        No         3
## 1066 Research & Development       Married    Life Sciences        No         4
## 1067 Research & Development       Married          Medical        No         4
## 1068                  Sales       Married          Medical        No         3
## 1069 Research & Development        Single          Medical       Yes         2
## 1070 Research & Development      Divorced    Life Sciences        No         3
## 1071                  Sales        Single    Life Sciences        No         3
## 1072 Research & Development       Married          Medical        No         2
## 1073 Research & Development       Married    Life Sciences        No         1
## 1074 Research & Development       Married    Life Sciences        No         1
## 1075 Research & Development        Single    Life Sciences        No         5
## 1076 Research & Development        Single          Medical        No         3
## 1077 Research & Development      Divorced          Medical        No         4
## 1078 Research & Development        Single Technical Degree       Yes         4
## 1079 Research & Development       Married    Life Sciences        No         3
## 1080 Research & Development        Single    Life Sciences        No         3
## 1081                  Sales       Married    Life Sciences        No         3
## 1082 Research & Development        Single    Life Sciences        No         3
## 1083 Research & Development        Single    Life Sciences        No         1
## 1084 Research & Development        Single    Life Sciences       Yes         4
## 1085                  Sales       Married Technical Degree        No         3
## 1086 Research & Development        Single    Life Sciences       Yes         3
## 1087 Research & Development        Single          Medical        No         5
## 1088                  Sales       Married Technical Degree        No         2
## 1089 Research & Development       Married          Medical        No         3
## 1090 Research & Development       Married          Medical        No         3
## 1091 Research & Development       Married            Other        No         1
## 1092 Research & Development        Single    Life Sciences        No         3
## 1093 Research & Development       Married Technical Degree        No         3
## 1094 Research & Development       Married    Life Sciences        No         3
## 1095                  Sales       Married          Medical        No         2
## 1096 Research & Development       Married    Life Sciences        No         4
## 1097        Human Resources        Single          Medical        No         2
## 1098 Research & Development      Divorced Technical Degree        No         2
## 1099 Research & Development      Divorced    Life Sciences        No         2
## 1100 Research & Development      Divorced Technical Degree        No         4
## 1101                  Sales       Married    Life Sciences        No         4
## 1102 Research & Development       Married    Life Sciences        No         2
## 1103                  Sales        Single    Life Sciences        No         4
## 1104                  Sales      Divorced    Life Sciences        No         4
## 1105 Research & Development       Married    Life Sciences        No         3
## 1106                  Sales       Married    Life Sciences        No         4
## 1107                  Sales       Married    Life Sciences       Yes         3
## 1108        Human Resources       Married  Human Resources        No         4
## 1109 Research & Development        Single          Medical        No         3
## 1110                  Sales       Married Technical Degree        No         4
## 1111 Research & Development      Divorced    Life Sciences       Yes         3
## 1112 Research & Development       Married Technical Degree       Yes         5
## 1113 Research & Development       Married          Medical       Yes         3
## 1114 Research & Development       Married Technical Degree        No         4
## 1115 Research & Development       Married            Other        No         4
## 1116 Research & Development        Single          Medical        No         4
## 1117                  Sales       Married        Marketing        No         5
## 1118 Research & Development       Married    Life Sciences        No         4
## 1119 Research & Development       Married    Life Sciences        No         3
## 1120                  Sales       Married    Life Sciences        No         3
## 1121                  Sales        Single    Life Sciences        No         3
## 1122                  Sales        Single    Life Sciences        No         4
## 1123 Research & Development        Single          Medical        No         1
## 1124 Research & Development        Single          Medical        No         4
## 1125                  Sales       Married          Medical        No         3
## 1126 Research & Development      Divorced    Life Sciences        No         1
## 1127                  Sales       Married        Marketing        No         3
## 1128 Research & Development       Married Technical Degree        No         3
## 1129 Research & Development       Married    Life Sciences        No         4
## 1130 Research & Development        Single            Other        No         2
## 1131 Research & Development       Married    Life Sciences        No         3
## 1132 Research & Development       Married Technical Degree        No         4
## 1133                  Sales       Married    Life Sciences        No         2
## 1134 Research & Development      Divorced Technical Degree        No         3
## 1135 Research & Development       Married    Life Sciences        No         2
## 1136                  Sales        Single    Life Sciences        No         4
## 1137 Research & Development       Married          Medical       Yes         3
## 1138 Research & Development       Married            Other        No         2
## 1139 Research & Development       Married          Medical        No         5
## 1140 Research & Development       Married            Other        No         4
## 1141 Research & Development      Divorced          Medical        No         3
## 1142 Research & Development       Married          Medical        No         3
## 1143 Research & Development        Single          Medical        No         5
## 1144                  Sales       Married        Marketing        No         3
## 1145                  Sales        Single            Other        No         4
## 1146 Research & Development       Married    Life Sciences        No         4
## 1147 Research & Development      Divorced    Life Sciences        No         4
## 1148 Research & Development       Married    Life Sciences        No         4
## 1149 Research & Development       Married          Medical        No         5
## 1150 Research & Development      Divorced            Other        No         3
## 1151 Research & Development       Married    Life Sciences        No         5
## 1152 Research & Development      Divorced          Medical        No         3
## 1153 Research & Development        Single          Medical        No         1
## 1154                  Sales        Single          Medical       Yes         2
## 1155        Human Resources       Married    Life Sciences        No         4
## 1156 Research & Development      Divorced          Medical        No         2
## 1157 Research & Development       Married    Life Sciences        No         3
## 1158 Research & Development       Married    Life Sciences        No         4
## 1159 Research & Development       Married    Life Sciences        No         3
## 1160 Research & Development        Single          Medical        No         3
## 1161 Research & Development      Divorced            Other        No         2
## 1162 Research & Development       Married          Medical        No         2
## 1163                  Sales       Married          Medical       Yes         3
## 1164 Research & Development       Married          Medical        No         3
## 1165 Research & Development        Single    Life Sciences        No         3
## 1166        Human Resources       Married  Human Resources        No         5
## 1167 Research & Development       Married          Medical        No         5
## 1168                  Sales      Divorced          Medical       Yes         2
## 1169 Research & Development        Single Technical Degree        No         1
## 1170 Research & Development       Married          Medical        No         3
## 1171 Research & Development        Single          Medical        No         3
## 1172 Research & Development        Single    Life Sciences       Yes         3
## 1173                  Sales        Single          Medical        No         3
## 1174 Research & Development       Married    Life Sciences        No         4
## 1175 Research & Development      Divorced    Life Sciences        No         1
## 1176 Research & Development       Married          Medical        No         3
## 1177 Research & Development       Married            Other        No         4
## 1178 Research & Development      Divorced    Life Sciences        No         5
## 1179                  Sales        Single          Medical        No         3
## 1180 Research & Development      Divorced    Life Sciences        No         3
## 1181 Research & Development        Single    Life Sciences        No         3
## 1182 Research & Development       Married    Life Sciences        No         1
## 1183 Research & Development       Married          Medical        No         4
## 1184 Research & Development      Divorced    Life Sciences        No         2
## 1185 Research & Development       Married          Medical        No         5
## 1186 Research & Development       Married    Life Sciences        No         2
## 1187                  Sales        Single            Other       Yes         4
## 1188 Research & Development       Married    Life Sciences        No         3
## 1189                  Sales      Divorced          Medical        No         3
## 1190                  Sales      Divorced          Medical        No         4
## 1191 Research & Development      Divorced          Medical        No         3
## 1192                  Sales       Married    Life Sciences        No         4
## 1193 Research & Development      Divorced          Medical        No         3
## 1194 Research & Development        Single          Medical        No         3
## 1195                  Sales      Divorced    Life Sciences        No         4
## 1196 Research & Development        Single    Life Sciences        No         3
## 1197                  Sales        Single    Life Sciences        No         2
## 1198                  Sales        Single    Life Sciences        No         1
## 1199                  Sales      Divorced    Life Sciences        No         3
## 1200 Research & Development       Married    Life Sciences        No         4
## 1201        Human Resources      Divorced    Life Sciences        No         3
## 1202 Research & Development        Single          Medical       Yes         1
## 1203 Research & Development       Married          Medical        No         2
## 1204 Research & Development       Married          Medical        No         4
## 1205                  Sales       Married          Medical       Yes         2
## 1206 Research & Development        Single    Life Sciences       Yes         4
## 1207 Research & Development        Single          Medical        No         3
## 1208 Research & Development      Divorced Technical Degree        No         3
## 1209 Research & Development       Married          Medical        No         2
## 1210 Research & Development      Divorced          Medical        No         4
## 1211 Research & Development       Married          Medical        No         3
## 1212                  Sales      Divorced          Medical        No         4
## 1213 Research & Development       Married    Life Sciences        No         3
## 1214                  Sales      Divorced    Life Sciences       Yes         3
## 1215 Research & Development       Married    Life Sciences        No         3
## 1216 Research & Development        Single          Medical        No         4
## 1217                  Sales       Married          Medical        No         3
## 1218 Research & Development       Married          Medical        No         3
## 1219                  Sales        Single        Marketing        No         3
## 1220 Research & Development       Married          Medical        No         4
## 1221                  Sales        Single    Life Sciences        No         4
## 1222 Research & Development       Married    Life Sciences        No         1
## 1223        Human Resources       Married  Human Resources       Yes         1
## 1224                  Sales       Married    Life Sciences       Yes         3
## 1225 Research & Development       Married          Medical        No         4
## 1226 Research & Development        Single Technical Degree        No         2
## 1227 Research & Development       Married    Life Sciences        No         3
## 1228 Research & Development       Married    Life Sciences        No         4
## 1229        Human Resources       Married  Human Resources        No         3
## 1230 Research & Development       Married    Life Sciences        No         2
## 1231 Research & Development      Divorced          Medical        No         1
## 1232 Research & Development        Single    Life Sciences        No         4
## 1233 Research & Development       Married    Life Sciences        No         4
## 1234 Research & Development       Married    Life Sciences        No         1
## 1235                  Sales       Married        Marketing        No         4
## 1236                  Sales      Divorced    Life Sciences        No         3
## 1237                  Sales      Divorced        Marketing       Yes         5
## 1238                  Sales        Single    Life Sciences       Yes         2
## 1239 Research & Development        Single          Medical        No         1
## 1240 Research & Development        Single Technical Degree        No         1
## 1241 Research & Development       Married    Life Sciences        No         3
## 1242                  Sales       Married    Life Sciences        No         3
## 1243                  Sales        Single          Medical        No         4
## 1244        Human Resources       Married    Life Sciences        No         3
## 1245 Research & Development        Single Technical Degree        No         4
## 1246        Human Resources       Married          Medical        No         3
## 1247        Human Resources      Divorced  Human Resources       Yes         3
## 1248                  Sales       Married Technical Degree        No         3
## 1249 Research & Development        Single          Medical        No         3
## 1250                  Sales        Single        Marketing       Yes         3
## 1251 Research & Development        Single    Life Sciences        No         3
## 1252                  Sales      Divorced        Marketing        No         2
## 1253 Research & Development       Married          Medical        No         4
## 1254                  Sales        Single        Marketing        No         3
## 1255                  Sales        Single        Marketing        No         4
## 1256                  Sales        Single    Life Sciences       Yes         3
## 1257 Research & Development       Married          Medical        No         2
## 1258                  Sales       Married        Marketing       Yes         4
## 1259 Research & Development      Divorced Technical Degree        No         3
## 1260 Research & Development       Married    Life Sciences        No         3
## 1261 Research & Development        Single Technical Degree        No         4
## 1262 Research & Development       Married          Medical        No         3
## 1263 Research & Development       Married Technical Degree       Yes         3
## 1264 Research & Development      Divorced          Medical        No         3
## 1265 Research & Development       Married          Medical        No         3
## 1266 Research & Development      Divorced Technical Degree        No         3
## 1267 Research & Development      Divorced    Life Sciences        No         4
## 1268                  Sales      Divorced    Life Sciences        No         3
## 1269 Research & Development       Married          Medical        No         4
## 1270        Human Resources        Single    Life Sciences        No         3
## 1271                  Sales        Single    Life Sciences        No         2
## 1272                  Sales        Single        Marketing       Yes         1
## 1273 Research & Development       Married            Other        No         2
## 1274 Research & Development       Married          Medical       Yes         1
## 1275                  Sales       Married        Marketing        No         4
## 1276 Research & Development       Married Technical Degree        No         3
## 1277                  Sales       Married        Marketing        No         2
## 1278 Research & Development      Divorced          Medical        No         4
## 1279 Research & Development       Married    Life Sciences        No         3
## 1280 Research & Development      Divorced          Medical       Yes         2
## 1281        Human Resources      Divorced            Other        No         2
## 1282                  Sales        Single    Life Sciences       Yes         3
## 1283 Research & Development       Married    Life Sciences        No         4
## 1284 Research & Development       Married    Life Sciences        No         3
## 1285 Research & Development        Single          Medical        No         1
## 1286                  Sales        Single    Life Sciences        No         2
## 1287 Research & Development       Married    Life Sciences        No         2
## 1288 Research & Development       Married          Medical        No         3
## 1289 Research & Development      Divorced          Medical        No         2
## 1290        Human Resources      Divorced  Human Resources        No         3
## 1291 Research & Development       Married    Life Sciences       Yes         4
## 1292 Research & Development        Single          Medical       Yes         4
## 1293                  Sales      Divorced    Life Sciences        No         3
## 1294 Research & Development        Single    Life Sciences        No         3
## 1295 Research & Development        Single    Life Sciences        No         3
## 1296                  Sales      Divorced        Marketing        No         1
## 1297 Research & Development        Single          Medical        No         3
## 1298        Human Resources       Married          Medical       Yes         2
## 1299 Research & Development       Married          Medical       Yes         2
## 1300 Research & Development      Divorced    Life Sciences        No         3
## 1301                  Sales       Married Technical Degree        No         2
## 1302                  Sales      Divorced          Medical        No         3
## 1303 Research & Development       Married          Medical        No         4
## 1304 Research & Development      Divorced    Life Sciences        No         3
## 1305 Research & Development      Divorced    Life Sciences        No         3
## 1306 Research & Development       Married          Medical        No         4
## 1307                  Sales       Married        Marketing        No         4
## 1308 Research & Development       Married          Medical        No         3
## 1309                  Sales       Married        Marketing        No         4
## 1310                  Sales        Single          Medical        No         3
## 1311 Research & Development       Married    Life Sciences        No         4
## 1312 Research & Development        Single          Medical        No         3
## 1313        Human Resources       Married  Human Resources       Yes         5
## 1314        Human Resources      Divorced  Human Resources       Yes         3
## 1315                  Sales       Married    Life Sciences        No         4
## 1316 Research & Development       Married            Other        No         4
## 1317                  Sales       Married    Life Sciences        No         4
## 1318 Research & Development        Single    Life Sciences        No         2
## 1319 Research & Development       Married          Medical        No         1
## 1320                  Sales        Single        Marketing        No         4
## 1321 Research & Development       Married Technical Degree        No         4
## 1322 Research & Development        Single    Life Sciences        No         4
## 1323 Research & Development      Divorced    Life Sciences        No         2
## 1324        Human Resources      Divorced    Life Sciences        No         2
## 1325 Research & Development      Divorced    Life Sciences        No         1
## 1326 Research & Development        Single    Life Sciences        No         3
## 1327                  Sales        Single        Marketing       Yes         4
## 1328                  Sales      Divorced Technical Degree        No         3
## 1329                  Sales       Married          Medical        No         1
## 1330        Human Resources       Married          Medical        No         1
## 1331 Research & Development       Married          Medical        No         3
## 1332 Research & Development       Married    Life Sciences        No         3
## 1333 Research & Development        Single    Life Sciences       Yes         2
## 1334                  Sales       Married    Life Sciences       Yes         3
## 1335 Research & Development       Married    Life Sciences        No         3
## 1336 Research & Development      Divorced            Other        No         4
## 1337 Research & Development       Married Technical Degree        No         4
## 1338                  Sales       Married          Medical        No         3
## 1339                  Sales        Single          Medical       Yes         3
## 1340 Research & Development        Single    Life Sciences       Yes         1
## 1341                  Sales       Married Technical Degree        No         4
## 1342 Research & Development      Divorced    Life Sciences        No         3
## 1343                  Sales       Married    Life Sciences        No         3
## 1344 Research & Development        Single    Life Sciences        No         3
## 1345 Research & Development       Married          Medical        No         4
## 1346 Research & Development       Married            Other        No         2
## 1347 Research & Development       Married    Life Sciences        No         2
## 1348        Human Resources        Single  Human Resources        No         1
## 1349 Research & Development      Divorced    Life Sciences        No         4
## 1350 Research & Development       Married    Life Sciences        No         2
## 1351                  Sales        Single          Medical        No         2
## 1352 Research & Development      Divorced          Medical        No         3
## 1353 Research & Development       Married    Life Sciences        No         4
## 1354 Research & Development       Married Technical Degree       Yes         4
## 1355 Research & Development        Single    Life Sciences       Yes         2
## 1356                  Sales       Married        Marketing        No         2
## 1357                  Sales       Married        Marketing        No         3
## 1358 Research & Development       Married          Medical        No         3
## 1359                  Sales      Divorced          Medical        No         2
## 1360                  Sales       Married          Medical        No         1
## 1361 Research & Development      Divorced          Medical        No         3
## 1362 Research & Development       Married            Other        No         3
## 1363 Research & Development        Single          Medical        No         4
## 1364                  Sales        Single        Marketing        No         4
## 1365                  Sales       Married    Life Sciences        No         2
## 1366                  Sales        Single Technical Degree       Yes         3
## 1367                  Sales       Married    Life Sciences        No         4
## 1368 Research & Development       Married Technical Degree        No         4
## 1369 Research & Development       Married            Other        No         4
## 1370                  Sales        Single        Marketing       Yes         2
## 1371 Research & Development       Married Technical Degree        No         4
## 1372                  Sales       Married        Marketing        No         5
## 1373 Research & Development       Married          Medical        No         2
## 1374 Research & Development      Divorced          Medical        No         3
## 1375                  Sales       Married    Life Sciences        No         3
## 1376 Research & Development        Single    Life Sciences       Yes         2
## 1377 Research & Development      Divorced    Life Sciences        No         2
## 1378 Research & Development       Married    Life Sciences        No         1
## 1379                  Sales      Divorced        Marketing        No         4
## 1380        Human Resources       Married  Human Resources       Yes         3
## 1381                  Sales       Married          Medical        No         4
## 1382 Research & Development        Single          Medical        No         3
## 1383 Research & Development      Divorced          Medical        No         2
## 1384 Research & Development       Married    Life Sciences        No         4
## 1385                  Sales        Single        Marketing        No         3
## 1386                  Sales      Divorced          Medical        No         4
## 1387 Research & Development        Single          Medical        No         3
## 1388 Research & Development       Married    Life Sciences        No         3
## 1389 Research & Development      Divorced          Medical        No         4
## 1390 Research & Development       Married    Life Sciences        No         3
## 1391 Research & Development      Divorced Technical Degree       Yes         3
## 1392                  Sales        Single    Life Sciences        No         3
## 1393                  Sales       Married    Life Sciences        No         4
## 1394                  Sales        Single        Marketing        No         3
## 1395 Research & Development        Single    Life Sciences        No         4
## 1396                  Sales       Married        Marketing       Yes         4
## 1397                  Sales        Single    Life Sciences       Yes         4
## 1398 Research & Development       Married    Life Sciences        No         2
## 1399 Research & Development      Divorced    Life Sciences        No         2
## 1400 Research & Development       Married    Life Sciences        No         3
## 1401        Human Resources       Married            Other        No         4
## 1402        Human Resources       Married  Human Resources        No         4
## 1403 Research & Development      Divorced          Medical        No         1
## 1404                  Sales        Single        Marketing        No         4
## 1405 Research & Development        Single    Life Sciences        No         2
## 1406 Research & Development       Married          Medical        No         3
## 1407 Research & Development        Single          Medical        No         3
## 1408 Research & Development        Single    Life Sciences        No         2
## 1409 Research & Development        Single            Other        No         2
## 1410 Research & Development       Married Technical Degree        No         3
## 1411                  Sales       Married        Marketing        No         2
## 1412        Human Resources       Married  Human Resources        No         3
## 1413 Research & Development       Married          Medical        No         2
## 1414 Research & Development      Divorced            Other        No         1
## 1415 Research & Development        Single          Medical        No         3
## 1416 Research & Development      Divorced          Medical        No         2
## 1417                  Sales       Married    Life Sciences        No         4
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## 1424 Research & Development        Single    Life Sciences        No         2
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## 1428 Research & Development       Married    Life Sciences        No         4
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## 1441 Research & Development      Divorced    Life Sciences        No         2
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## 1456 Research & Development        Single    Life Sciences        No         4
## 1457 Research & Development       Married    Life Sciences        No         4
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## 1465                  Sales        Single            Other        No         3
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## 1467 Research & Development       Married          Medical        No         1
## 1468 Research & Development       Married    Life Sciences        No         3
## 1469                  Sales       Married          Medical        No         3
## 1470 Research & Development       Married          Medical        No         3
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## 1084                9                       4               1  40          2018
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## 1092               25                       4               2  33          4320
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## 1095                9                       1               1  40          5473
## 1096               28                       2               3  33          5207
## 1097                6                       3               4  40         16437
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## 1111                2                       1               1  35          2074
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## 1135                7                       3               4  35          2690
## 1136                1                       4               1  46         17567
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## 1138               26                       2               3  22          2814
## 1139               20                       2               3  50         11245
## 1140                5                       2               4  32          3312
## 1141                7                       2               4  44         19049
## 1142                7                       2               2  30          2141
## 1143                5                       3               1  45          5769
## 1144               26                       1               1  45          4385
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## 1159               19                       3               3  37          5768
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## 1164               10                       2               2  37          3936
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## 1167                4                       3               4  48         15202
## 1168               15                       1               4  35          5440
## 1169                2                       1               4  24          3760
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## 1172                7                       1               1  40          2166
## 1173               10                       3               3  29          5869
## 1174                5                       2               1  36          8008
## 1175                2                       4               3  25          5206
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## 1179                2                       3               3  20          2783
## 1180                3                       4               2  34          5433
## 1181                7                       1               2  36          2013
## 1182                6                       3               3  49         13966
## 1183                1                       4               3  36          4374
## 1184                3                       4               1  36          6842
## 1185               22                       2               3  54         17426
## 1186               15                       3               3  43         17603
## 1187               12                       4               4  35          4581
## 1188                1                       4               4  38          4735
## 1189                5                       1               2  29          4187
## 1190                2                       4               4  33          5505
## 1191                2                       4               2  32          5470
## 1192                5                       1               4  31          5476
## 1193               16                       4               1  49          2587
## 1194                2                       4               2  38          2440
## 1195                2                       2               2  47         15972
## 1196                1                       3               3  49         15379
## 1197               23                       4               3  41          7082
## 1198                9                       4               1  20          2728
## 1199               16                       3               4  33          5368
## 1200               26                       1               3  36          5347
## 1201                1                       3               4  44          3195
## 1202                8                       4               3  23          3989
## 1203                4                       4               3  38          3306
## 1204               24                       2               4  53          7005
## 1205                7                       4               3  48          2655
## 1206                2                       4               2  32          1393
## 1207                7                       4               4  26          2570
## 1208               22                       1               2  55          3537
## 1209                5                       2               4  34          3986
## 1210                1                       3               4  60         10883
## 1211               21                       2               2  33          2028
## 1212                1                       3               4  37          9525
## 1213               19                       2               4  34          2929
## 1214                7                       3               4  23          2275
## 1215                2                       3               4  44          7879
## 1216                2                       1               4  35          4930
## 1217                2                       4               4  43          7847
## 1218                9                       3               3  24          4401
## 1219                6                       4               3  41          9241
## 1220                9                       4               3  29          2974
## 1221                2                       3               4  36          4502
## 1222                1                       3               3  45         10748
## 1223               22                       4               3  24          1555
## 1224                9                       3               3  47         12936
## 1225               17                       4               3  26          2305
## 1226               28                       4               2  45         16704
## 1227               10                       1               3  32          3433
## 1228                2                       2               3  31          3477
## 1229                4                       3               2  41          6430
## 1230                8                       2               1  40          6516
## 1231               29                       2               1  24          3907
## 1232               13                       3               2  46          5562
## 1233               27                       4               3  35          6883
## 1234               16                       2               4  30          2862
## 1235                2                       3               2  47          4978
## 1236                2                       3               4  46         10368
## 1237               13                       2               1  36          6134
## 1238                1                       1               2  32          6735
## 1239                4                       3               2  23          3295
## 1240               24                       4               4  31          5238
## 1241                1                       4               4  39          6472
## 1242               19                       4               3  32          9610
## 1243                7                       2               2  40         19833
## 1244                4                       3               3  45          9756
## 1245                2                       4               1  30          4968
## 1246               10                       1               4  24          2145
## 1247                8                       3               4  30          2180
## 1248                5                       1               3  31          8346
## 1249                8                       3               4  27          3445
## 1250                9                       2               2  29          2760
## 1251                1                       4               3  29          6294
## 1252               15                       3               1  30          7140
## 1253                2                       4               4  34          2932
## 1254                2                       4               2  33          5147
## 1255               11                       4               4  49          4507
## 1256               16                       1               1  33          8564
## 1257                2                       3               2  38          2468
## 1258               16                       1               3  31          8161
## 1259                4                       4               1  29          2109
## 1260               16                       3               3  30          5294
## 1261                5                       2               2  32          2718
## 1262               18                       2               4  38          5811
## 1263               17                       3               3  43          2437
## 1264               12                       2               2  42          2766
## 1265                2                       3               1  55         19038
## 1266                4                       4               2  33          3055
## 1267                9                       3               1  41          2289
## 1268               10                       4               3  34          4001
## 1269                1                       1               3  53         12965
## 1270                2                       2               4  43          3539
## 1271                3                       4               4  34          6029
## 1272                7                       2               2  21          2679
## 1273                6                       4               3  38          3702
## 1274                8                       3               1  22          2398
## 1275               29                       1               4  31          5468
## 1276                3                       1               3  51         13116
## 1277                9                       2               2  37          4189
## 1278                2                       3               4  46         19328
## 1279               10                       4               1  36          8321
## 1280                1                       3               2  44          2342
## 1281                8                       3               2  37          4071
## 1282               27                       3               4  35          5813
## 1283                8                       4               1  33          3143
## 1284                1                       3               4  28          2044
## 1285               10                       3               3  39         13464
## 1286               26                       2               2  46          7991
## 1287                2                       3               1  40          3377
## 1288               13                       2               1  42          5538
## 1289                2                       2               4  35          5762
## 1290                2                       1               2  38          2592
## 1291                9                       4               1  34          5346
## 1292               10                       4               1  37          4213
## 1293               20                       3               4  39          4127
## 1294                9                       1               3  43          2438
## 1295                5                       2               2  41          6870
## 1296                4                       3               3  41         10447
## 1297               10                       1               3  30          9667
## 1298               20                       4               2  26          2148
## 1299               21                       4               2  46          8926
## 1300                1                       3               4  40          6513
## 1301                8                       2               3  34          6799
## 1302                2                       2               2  58         16291
## 1303               23                       2               3  35          2705
## 1304                4                       3               2  47         10333
## 1305               12                       2               1  40          4448
## 1306                7                       4               4  54          6854
## 1307                7                       1               1  31          9637
## 1308                1                       3               1  28          3591
## 1309                2                       2               4  38          5405
## 1310               10                       3               4  26          4684
## 1311               15                       1               3  58         15787
## 1312               14                       2               3  18          1514
## 1313               18                       4               1  31          2956
## 1314               13                       1               1  29          2335
## 1315                2                       3               3  45          5154
## 1316                2                       4               2  36          6962
## 1317                2                       1               4  43          5675
## 1318                5                       4               4  27          2379
## 1319               20                       4               4  29          3812
## 1320               10                       4               4  32          4648
## 1321               10                       3               3  42          2936
## 1322                9                       2               3  47          2105
## 1323                2                       4               4  46          8578
## 1324                1                       3               4  28          2706
## 1325               29                       4               3  29          6384
## 1326                8                       4               3  42          3968
## 1327                2                       3               2  32          9907
## 1328                3                       1               1  46         13225
## 1329               23                       2               3  27          3540
## 1330                6                       4               2  29          2804
## 1331                6                       1               3  43         19392
## 1332               10                       4               2  48         19665
## 1333               24                       4               4  29          2439
## 1334               10                       3               2  46          7314
## 1335               15                       4               1  27          4774
## 1336               19                       4               4  39          3902
## 1337                2                       2               4  55          2662
## 1338                3                       2               2  28          2856
## 1339                9                       2               4  30          1081
## 1340                7                       4               2  22          2472
## 1341               10                       2               3  36          5673
## 1342               20                       2               3  31          4197
## 1343                4                       3               4  34          9713
## 1344                7                       4               1  29          2062
## 1345                7                       4               1  37          4284
## 1346               16                       4               2  35          4788
## 1347               25                       2               4  45          5906
## 1348                2                       2               4  36          3886
## 1349                1                       1               1  40         16823
## 1350                1                       2               3  26          2933
## 1351                2                       1               3  27          6500
## 1352               22                       4               4  48         17174
## 1353                1                       2               1  44          5033
## 1354               16                       4               1  34          2307
## 1355               24                       1               4  56          2587
## 1356               17                       3               2  36          5507
## 1357                8                       3               2  41          4393
## 1358                6                       3               1  42         13348
## 1359               10                       3               4  31          6583
## 1360                3                       4               4  34          8103
## 1361                4                       1               3  31          3978
## 1362                6                       3               4  26          2544
## 1363                1                       2               3  45          5399
## 1364               10                       2               3  33          5487
## 1365                1                       3               4  28          6834
## 1366               24                       3               1  29          1091
## 1367               21                       1               3  39          5736
## 1368                2                       2               2  27          2226
## 1369               22                       3               4  34          5747
## 1370               13                       4               3  28          9854
## 1371               14                       3               2  47          5467
## 1372               11                       4               1  56          5380
## 1373                9                       1               1  39          5151
## 1374                8                       4               2  38          2133
## 1375               21                       4               4  58         17875
## 1376                5                       1               3  32          2432
## 1377                9                       2               4  38          4771
## 1378                2                       2               4  49         19161
## 1379               12                       2               4  42          5087
## 1380               22                       1               2  27          2863
## 1381               18                       2               1  35          5561
## 1382               16                       3               3  28          2144
## 1383                3                       3               1  31          3065
## 1384                9                       1               2  36          2810
## 1385                1                       1               4  34          9888
## 1386               13                       4               3  34          8628
## 1387                1                       3               1  26          2867
## 1388                1                       1               1  29          5373
## 1389               15                       3               4  32          6667
## 1390                1                       4               1  31          5003
## 1391               17                       3               4  28          2367
## 1392                1                       1               1  38          2858
## 1393                7                       3               4  35          5204
## 1394                9                       4               4  27          4105
## 1395                5                       4               4  32          9679
## 1396               26                       1               4  31          5617
## 1397               24                       1               1  53         10448
## 1398                9                       1               3  54          2897
## 1399                7                       4               3  33          5968
## 1400               11                       1               3  43          7510
## 1401                1                       4               2  38          2991
## 1402               26                       3               2  55         19636
## 1403                2                       4               4  31          1129
## 1404               15                       2               1  39         13341
## 1405               23                       4               3  42          4332
## 1406               10                       3               3  31         11031
## 1407               10                       3               1  54          4440
## 1408                1                       2               3  24          4617
## 1409               12                       4               4  23          2647
## 1410               11                       4               3  40          6323
## 1411                2                       2               2  40          5677
## 1412                2                       3               2  25          2187
## 1413                1                       4               2  30          3748
## 1414                2                       4               3  25          3977
## 1415               25                       1               3  47          8633
## 1416                1                       2               3  33          2008
## 1417                1                       4               2  38          4440
## 1418                2                       1               3  31          3067
## 1419                6                       1               3  38          5321
## 1420               18                       4               1  42          5410
## 1421                1                       4               4  41          2782
## 1422                1                       3               2  47         11957
## 1423               11                       4               3  35          2660
## 1424                1                       4               3  22          3375
## 1425                9                       2               3  35          5098
## 1426               15                       2               4  33          4878
## 1427               29                       3               2  32          2837
## 1428                1                       1               4  40          2406
## 1429                1                       2               2  32          2269
## 1430               24                       1               4  39          4108
## 1431               10                       2               3  38         13206
## 1432                1                       3               4  32         10422
## 1433               10                       3               4  37         13744
## 1434                8                       1               3  25          4907
## 1435               29                       1               4  52          3482
## 1436                1                       2               4  44          2436
## 1437                5                       3               1  21          2380
## 1438                9                       4               4  39         19431
## 1439                9                       4               1  23          1790
## 1440                3                       1               4  36          7644
## 1441                4                       4               2  36          5131
## 1442                1                       3               3  56          6306
## 1443                1                       1               4  29          4787
## 1444                2                       1               3  42         18880
## 1445                7                       4               3  56          2339
## 1446               28                       1               2  41         13570
## 1447               28                       4               3  34          6712
## 1448               15                       4               4  36          5406
## 1449                3                       3               2  41          8938
## 1450                2                       4               1  32          2439
## 1451               26                       3               4  35          8837
## 1452               10                       1               4  38          5343
## 1453                1                       2               3  50          6728
## 1454               11                       2               4  36          6652
## 1455               20                       4               3  45          4850
## 1456                2                       3               3  40          2809
## 1457               18                       3               3  35          5689
## 1458                2                       3               3  40          2001
## 1459                1                       3               4  35          2977
## 1460               13                       4               2  29          4025
## 1461               28                       4               1  29          3785
## 1462               28                       4               1  50         10854
## 1463               24                       2               4  39         12031
## 1464                5                       2               1  31          9936
## 1465                5                       4               3  26          2966
## 1466               23                       3               4  36          2571
## 1467                6                       4               1  39          9991
## 1468                4                       2               2  27          6142
## 1469                2                       4               2  49          5390
## 1470                8                       2               3  34          4404
##      NumCompaniesWorked WorkLifeBalance YearsAtCompany
## 1                     8               1              6
## 2                     1               3             10
## 3                     6               3              0
## 4                     1               3              8
## 5                     9               3              2
## 6                     0               2              7
## 7                     4               2              1
## 8                     1               3              1
## 9                     0               3              9
## 10                    6               2              7
## 11                    0               3              5
## 12                    0               3              9
## 13                    1               2              5
## 14                    0               3              2
## 15                    5               3              4
## 16                    1               3             10
## 17                    0               2              6
## 18                    1               2              1
## 19                    2               3             25
## 20                    5               3              3
## 21                    0               2              4
## 22                    7               3              5
## 23                    0               3             12
## 24                    1               3              0
## 25                    2               3              4
## 26                    4               2             14
## 27                    1               3             10
## 28                    0               3              9
## 29                    3               3             22
## 30                    3               2              2
## 31                    4               3              1
## 32                    2               4              4
## 33                    1               3             10
## 34                    3               4              1
## 35                    2               2              2
## 36                    1               2              5
## 37                    1               3              3
## 38                    1               3              2
## 39                    9               4              1
## 40                    2               3              5
## 41                    1               3              1
## 42                    1               3              1
## 43                    1               2              1
## 44                    1               3              9
## 45                    1               3             12
## 46                    1               3             22
## 47                    0               3              9
## 48                    4               3              1
## 49                    4               3              9
## 50                    1               3              1
## 51                    9               3              1
## 52                    1               2              2
## 53                    5               2              4
## 54                    2               3              4
## 55                    7               2              2
## 56                    1               3             15
## 57                    1               2              9
## 58                    3               3              2
## 59                    3               2              7
## 60                    1               4              7
## 61                    1               3              9
## 62                    1               3             10
## 63                    5               2             27
## 64                    7               2             21
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head(attrition_data)

##               Department MaritalStatus EducationField Attrition Education
## 1                  Sales        Single  Life Sciences       Yes         2
## 2 Research & Development       Married  Life Sciences        No         1
## 3 Research & Development        Single          Other       Yes         2
## 4 Research & Development       Married  Life Sciences        No         4
## 5 Research & Development       Married        Medical        No         1
## 6 Research & Development        Single  Life Sciences        No         2
##   DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age MonthlyIncome
## 1                1                       2               4  41          5993
## 2                8                       3               2  49          5130
## 3                2                       4               3  37          2090
## 4                3                       4               3  33          2909
## 5                2                       1               2  27          3468
## 6                2                       4               4  32          3068
##   NumCompaniesWorked WorkLifeBalance YearsAtCompany
## 1                  8               1              6
## 2                  1               3             10
## 3                  6               3              0
## 4                  1               3              8
## 5                  9               3              2
## 6                  0               2              7

str(attrition_data)

## 'data.frame':    1470 obs. of  13 variables:
##  $ Department             : chr  "Sales" "Research & Development" "Research & Development" "Research & Development" ...
##  $ MaritalStatus          : chr  "Single" "Married" "Single" "Married" ...
##  $ EducationField         : chr  "Life Sciences" "Life Sciences" "Other" "Life Sciences" ...
##  $ Attrition              : chr  "Yes" "No" "Yes" "No" ...
##  $ Education              : int  2 1 2 4 1 2 3 1 3 3 ...
##  $ DistanceFromHome       : int  1 8 2 3 2 2 3 24 23 27 ...
##  $ EnvironmentSatisfaction: int  2 3 4 4 1 4 3 4 4 3 ...
##  $ JobSatisfaction        : int  4 2 3 3 2 4 1 3 3 3 ...
##  $ Age                    : int  41 49 37 33 27 32 59 30 38 36 ...
##  $ MonthlyIncome          : int  5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
##  $ NumCompaniesWorked     : int  8 1 6 1 9 0 4 1 0 6 ...
##  $ WorkLifeBalance        : int  1 3 3 3 3 2 2 3 3 2 ...
##  $ YearsAtCompany         : int  6 10 0 8 2 7 1 1 9 7 ...

#Converting necessary columns into Factors

attrition_data$Attrition <- as.factor(attrition_data$Attrition)
attrition_data$Education <- as.factor(attrition_data$Education)
attrition_data$JobSatisfaction <- as.factor(attrition_data$JobSatisfaction)
attrition_data$EnvironmentSatisfaction <- as.factor(attrition_data$EnvironmentSatisfaction)
attrition_data$WorkLifeBalance <- as.factor(attrition_data$WorkLifeBalance)

nrow(attrition_data)

## [1] 1470

## Exploratory Analysis

xtabs(~ Attrition + Education, data=attrition_data)

##          Education
## Attrition   1   2   3   4   5
##       No  139 238 473 340  43
##       Yes  31  44  99  58   5

xtabs(~ Attrition + JobSatisfaction, data=attrition_data)

##          JobSatisfaction
## Attrition   1   2   3   4
##       No  223 234 369 407
##       Yes  66  46  73  52

xtabs(~ Attrition + EnvironmentSatisfaction, data=attrition_data)

##          EnvironmentSatisfaction
## Attrition   1   2   3   4
##       No  212 244 391 386
##       Yes  72  43  62  60

xtabs(~ Attrition + WorkLifeBalance, data=attrition_data)

##          WorkLifeBalance
## Attrition   1   2   3   4
##       No   55 286 766 126
##       Yes  25  58 127  27

#Model Development

logistic_simple <- glm(Attrition ~ Education+JobSatisfaction+EnvironmentSatisfaction+WorkLifeBalance, data=attrition_data, family="binomial")
summary(logistic_simple)

## 
## Call:
## glm(formula = Attrition ~ Education + JobSatisfaction + EnvironmentSatisfaction + 
##     WorkLifeBalance, family = "binomial", data = attrition_data)
## 
## Coefficients:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                0.4331     0.3666   1.181 0.237417    
## Education2                -0.2516     0.2629  -0.957 0.338485    
## Education3                -0.1436     0.2325  -0.618 0.536755    
## Education4                -0.3577     0.2496  -1.433 0.151752    
## Education5                -0.7242     0.5195  -1.394 0.163266    
## JobSatisfaction2          -0.4294     0.2176  -1.973 0.048489 *  
## JobSatisfaction3          -0.4494     0.1939  -2.317 0.020490 *  
## JobSatisfaction4          -0.8619     0.2067  -4.169 3.05e-05 ***
## EnvironmentSatisfaction2  -0.6427     0.2186  -2.940 0.003287 ** 
## EnvironmentSatisfaction3  -0.7754     0.1971  -3.934 8.35e-05 ***
## EnvironmentSatisfaction4  -0.7856     0.1983  -3.961 7.45e-05 ***
## WorkLifeBalance2          -0.7712     0.2886  -2.673 0.007529 ** 
## WorkLifeBalance3          -0.9864     0.2666  -3.700 0.000216 ***
## WorkLifeBalance4          -0.7186     0.3291  -2.184 0.028982 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1298.6  on 1469  degrees of freedom
## Residual deviance: 1243.5  on 1456  degrees of freedom
## AIC: 1271.5
## 
## Number of Fisher Scoring iterations: 4

#Most of the predictor variables ("Education", "JobSatisfaction", etc.) have coefficients with statistically significant p-values (all p-values are greater than alpha). This suggests that there is insufficient evidence to conclude that any of these variables have a significant impact on Attrition.


predicted.attrition_data <- data.frame(probability.of.Attrition=logistic_simple$fitted.values,JobSatisfaction=attrition_data$JobSatisfaction)
predicted.attrition_data

##      probability.of.Attrition JobSatisfaction
## 1                  0.21030618               4
## 2                  0.14703800               2
## 3                  0.11506678               3
## 4                  0.10469892               3
## 5                  0.27236401               2
## 6                  0.09645536               4
## 7                  0.22147291               1
## 8                  0.14327491               3
## 9                  0.12652919               3
## 10                 0.15361462               3
## 11                 0.24484248               2
## 12                 0.11506678               3
## 13                 0.31270240               3
## 14                 0.09033978               4
## 15                 0.12766776               3
## 16                 0.17455487               1
## 17                 0.26520316               2
## 18                 0.09645536               4
## 19                 0.14518166               4
## 20                 0.08750724               4
## 21                 0.26131149               3
## 22                 0.15625192               1
## 23                 0.20744743               2
## 24                 0.08001127               4
## 25                 0.23219394               1
## 26                 0.15361462               3
## 27                 0.23219394               1
## 28                 0.10757604               2
## 29                 0.14518166               4
## 30                 0.20776140               1
## 31                 0.08833018               4
## 32                 0.09189219               4
## 33                 0.11506678               3
## 34                 0.11138440               4
## 35                 0.12065055               4
## 36                 0.13886031               3
## 37                 0.22194381               3
## 38                 0.08750724               4
## 39                 0.21654717               1
## 40                 0.18659103               1
## 41                 0.08001127               4
## 42                 0.15490370               1
## 43                 0.28268836               3
## 44                 0.12652919               3
## 45                 0.08001127               4
## 46                 0.14319066               3
## 47                 0.11887699               3
## 48                 0.13273719               2
## 49                 0.14518166               4
## 50                 0.09967788               4
## 51                 0.22194381               3
## 52                 0.12779496               3
## 53                 0.15381401               1
## 54                 0.17075120               1
## 55                 0.10726525               4
## 56                 0.15884708               4
## 57                 0.15381401               1
## 58                 0.15625192               1
## 59                 0.08759845               4
## 60                 0.25111676               3
## 61                 0.17381408               4
## 62                 0.05092901               4
## 63                 0.15685397               3
## 64                 0.38184110               1
## 65                 0.12766776               3
## 66                 0.12652919               3
## 67                 0.14567009               2
## 68                 0.20757354               1
## 69                 0.24519554               1
## 70                 0.15228505               3
## 71                 0.31270240               3
## 72                 0.12991915               2
## 73                 0.10757604               2
## 74                 0.14567009               2
## 75                 0.09961629               4
## 76                 0.07254308               4
## 77                 0.15625192               1
## 78                 0.19327547               1
## 79                 0.25111676               3
## 80                 0.13273719               2
## 81                 0.12072341               4
## 82                 0.14319066               3
## 83                 0.15884708               4
## 84                 0.09961629               4
## 85                 0.22542811               2
## 86                 0.10628647               4
## 87                 0.20938028               1
## 88                 0.07185564               4
## 89                 0.08833018               4
## 90                 0.08001127               4
## 91                 0.13004827               2
## 92                 0.17338087               4
## 93                 0.14252674               2
## 94                 0.22147291               1
## 95                 0.11887699               3
## 96                 0.40756665               3
## 97                 0.26131149               3
## 98                 0.17927647               3
## 99                 0.12665543               3
## 100                0.18224783               2
## 101                0.15625192               1
## 102                0.20768648               1
## 103                0.08750724               4
## 104                0.20416779               3
## 105                0.10207188               4
## 106                0.07254308               4
## 107                0.28677480               2
## 108                0.12766776               3
## 109                0.09967788               4
## 110                0.09961629               4
## 111                0.33274172               1
## 112                0.24115153               3
## 113                0.08750724               4
## 114                0.16173318               3
## 115                0.10757604               2
## 116                0.08833018               4
## 117                0.18659103               1
## 118                0.09033978               4
## 119                0.15884708               4
## 120                0.10207188               4
## 121                0.28268836               3
## 122                0.14907297               2
## 123                0.12099487               2
## 124                0.24115153               3
## 125                0.14333080               3
## 126                0.15624163               2
## 127                0.08759845               4
## 128                0.17176915               3
## 129                0.10060266               4
## 130                0.18676438               1
## 131                0.14319066               3
## 132                0.08833018               4
## 133                0.14319066               3
## 134                0.14453923               3
## 135                0.14453923               3
## 136                0.13273719               2
## 137                0.14518166               4
## 138                0.13258540               3
## 139                0.24115153               3
## 140                0.20623294               4
## 141                0.39432427               1
## 142                0.10726525               4
## 143                0.07498000               3
## 144                0.28268836               3
## 145                0.10113511               4
## 146                0.18503844               1
## 147                0.11326204               4
## 148                0.21970847               1
## 149                0.15625192               1
## 150                0.16447205               2
## 151                0.14567009               2
## 152                0.07711078               2
## 153                0.28687219               3
## 154                0.31376827               2
## 155                0.09961629               4
## 156                0.14327491               3
## 157                0.11887699               3
## 158                0.17454363               2
## 159                0.08842216               4
## 160                0.10566481               3
## 161                0.10060266               4
## 162                0.28383368               2
## 163                0.20623294               4
## 164                0.18911336               4
## 165                0.15361462               3
## 166                0.12991915               2
## 167                0.24115153               3
## 168                0.09961629               4
## 169                0.18166283               4
## 170                0.07569490               3
## 171                0.15624163               2
## 172                0.25714060               1
## 173                0.14127712               2
## 174                0.18659103               1
## 175                0.21206354               1
## 176                0.18659103               1
## 177                0.11240423               4
## 178                0.12065055               4
## 179                0.19036936               1
## 180                0.08001127               4
## 181                0.10060266               4
## 182                0.11712579               2
## 183                0.15952594               2
## 184                0.15361462               3
## 185                0.16930298               1
## 186                0.12876347               2
## 187                0.14327491               3
## 188                0.10757604               2
## 189                0.17176915               3
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## 191                0.10566481               3
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## 195                0.15884708               4
## 196                0.24519554               1
## 197                0.14567009               2
## 198                0.11611591               3
## 199                0.10469892               3
## 200                0.20455801               4
## 201                0.20938028               1
## 202                0.07185564               4
## 203                0.13258540               3
## 204                0.10207188               4
## 205                0.23219394               1
## 206                0.12065055               4
## 207                0.15489348               2
## 208                0.11326204               4
## 209                0.12579750               4
## 210                0.15490370               1
## 211                0.08759845               4
## 212                0.14453923               3
## 213                0.12652919               3
## 214                0.26960447               2
## 215                0.18503844               1
## 216                0.08750724               4
## 217                0.18676438               1
## 218                0.15361462               3
## 219                0.08750724               4
## 220                0.18503844               1
## 221                0.14777584               2
## 222                0.10757604               2
## 223                0.09961629               4
## 224                0.28268836               3
## 225                0.10566481               3
## 226                0.08833018               4
## 227                0.14518166               4
## 228                0.11326204               4
## 229                0.16057474               3
## 230                0.12181702               4
## 231                0.10726525               4
## 232                0.08001127               4
## 233                0.15685397               3
## 234                0.08759845               4
## 235                0.20623294               4
## 236                0.08750724               4
## 237                0.36884638               1
## 238                0.25111676               3
## 239                0.11819119               2
## 240                0.27977271               3
## 241                0.10566481               3
## 242                0.07254308               4
## 243                0.20341245               1
## 244                0.15884708               4
## 245                0.08833018               4
## 246                0.11887699               3
## 247                0.08842216               4
## 248                0.15490370               1
## 249                0.20341245               1
## 250                0.20416779               3
## 251                0.24115153               3
## 252                0.10566481               3
## 253                0.08833018               4
## 254                0.16930298               1
## 255                0.07925909               4
## 256                0.24115153               3
## 257                0.18503844               1
## 258                0.22194381               3
## 259                0.10726525               4
## 260                0.14907297               2
## 261                0.31376827               2
## 262                0.07925909               4
## 263                0.20768648               1
## 264                0.15624163               2
## 265                0.40756665               3
## 266                0.24484248               2
## 267                0.09961629               4
## 268                0.19036936               1
## 269                0.08001127               4
## 270                0.08750724               4
## 271                0.18503844               1
## 272                0.24505364               2
## 273                0.10628647               4
## 274                0.09275217               4
## 275                0.14526667               3
## 276                0.14518166               4
## 277                0.17454363               2
## 278                0.30896762               1
## 279                0.28592439               2
## 280                0.31703095               2
## 281                0.12779496               3
## 282                0.16173318               3
## 283                0.10965384               4
## 284                0.09033978               4
## 285                0.30896762               1
## 286                0.08750724               4
## 287                0.27977271               3
## 288                0.07185564               4
## 289                0.20744743               2
## 290                0.07925909               4
## 291                0.15625192               1
## 292                0.12991915               2
## 293                0.15489348               2
## 294                0.07185564               4
## 295                0.12065055               4
## 296                0.16329781               2
## 297                0.12766776               3
## 298                0.15624163               2
## 299                0.07254308               4
## 300                0.12876347               2
## 301                0.10659476               2
## 302                0.12652919               3
## 303                0.19036936               1
## 304                0.12065055               4
## 305                0.10726525               4
## 306                0.12099487               2
## 307                0.15228505               3
## 308                0.22542811               2
## 309                0.10469892               3
## 310                0.07254308               4
## 311                0.33248828               1
## 312                0.33248828               1
## 313                0.17338087               4
## 314                0.10659476               2
## 315                0.20938028               1
## 316                0.07254308               4
## 317                0.11611591               3
## 318                0.13004827               2
## 319                0.15624163               2
## 320                0.11819119               2
## 321                0.12652919               3
## 322                0.08750724               4
## 323                0.17397810               4
## 324                0.17397810               4
## 325                0.07925909               4
## 326                0.11611591               3
## 327                0.08001127               4
## 328                0.13886031               3
## 329                0.12065055               4
## 330                0.07498000               3
## 331                0.13377012               3
## 332                0.14703800               2
## 333                0.12665543               3
## 334                0.22147291               1
## 335                0.07185564               4
## 336                0.10965384               4
## 337                0.20776140               1
## 338                0.05829984               4
## 339                0.12652919               3
## 340                0.12099487               2
## 341                0.09645536               4
## 342                0.08001127               4
## 343                0.08842216               4
## 344                0.14575555               2
## 345                0.10757604               2
## 346                0.12181702               4
## 347                0.12876347               2
## 348                0.16173318               3
## 349                0.10532347               4
## 350                0.15228505               3
## 351                0.14453923               3
## 352                0.12991915               2
## 353                0.49592148               3
## 354                0.18659103               1
## 355                0.14526667               3
## 356                0.12766776               3
## 357                0.14518166               4
## 358                0.27236401               2
## 359                0.05092901               4
## 360                0.14518166               4
## 361                0.10469892               3
## 362                0.10469892               3
## 363                0.18975235               4
## 364                0.12652919               3
## 365                0.18659103               1
## 366                0.13377012               3
## 367                0.24484248               2
## 368                0.08750724               4
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## 380                0.08833018               4
## 381                0.13258540               3
## 382                0.14703800               2
## 383                0.20938028               1
## 384                0.24484248               2
## 385                0.13044428               3
## 386                0.08833018               4
## 387                0.21970847               1
## 388                0.11712579               2
## 389                0.17455487               1
## 390                0.13004827               2
## 391                0.24484248               2
## 392                0.14319066               3
## 393                0.35669477               1
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## 395                0.38670129               1
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## 418                0.10566481               3
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## 420                0.20623294               4
## 421                0.11887699               3
## 422                0.09845726               2
## 423                0.19796686               4
## 424                0.15625192               1
## 425                0.20691501               4
## 426                0.11887699               3
## 427                0.10726525               4
## 428                0.23066969               1
## 429                0.15884708               4
## 430                0.46009399               3
## 431                0.12652919               3
## 432                0.10566481               3
## 433                0.10469892               3
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## 436                0.20139355               3
## 437                0.19541773               4
## 438                0.14575555               2
## 439                0.12652919               3
## 440                0.24115153               3
## 441                0.20757354               1
## 442                0.13044428               3
## 443                0.09971874               4
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## 481                0.21654717               1
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## 483                0.36186670               1
## 484                0.15884708               4
## 485                0.18166283               4
## 486                0.24136052               3
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## 503                0.25518514               1
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## 513                0.14518166               4
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## 522                0.09967788               4
## 523                0.07925909               4
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## 620                0.33248828               1
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## 1236               0.10726525               4
## 1237               0.12783856               1
## 1238               0.22542811               2
## 1239               0.31613059               2
## 1240               0.12072341               4
## 1241               0.08750724               4
## 1242               0.27977271               3
## 1243               0.14581224               2
## 1244               0.16057474               3
## 1245               0.15490370               1
## 1246               0.17381408               4
## 1247               0.10726525               4
## 1248               0.24115153               3
## 1249               0.10726525               4
## 1250               0.14567009               2
## 1251               0.15919626               3
## 1252               0.17075120               1
## 1253               0.07185564               4
## 1254               0.15489348               2
## 1255               0.09189219               4
## 1256               0.38184110               1
## 1257               0.14252674               2
## 1258               0.20416779               3
## 1259               0.18503844               1
## 1260               0.12766776               3
## 1261               0.12099487               2
## 1262               0.09961629               4
## 1263               0.12766776               3
## 1264               0.17454363               2
## 1265               0.18659103               1
## 1266               0.15489348               2
## 1267               0.15625192               1
## 1268               0.12652919               3
## 1269               0.24136052               3
## 1270               0.09961629               4
## 1271               0.07925909               4
## 1272               0.16447205               2
## 1273               0.11506678               3
## 1274               0.20938028               1
## 1275               0.14518166               4
## 1276               0.24115153               3
## 1277               0.13273719               2
## 1278               0.07254308               4
## 1279               0.18503844               1
## 1280               0.14252674               2
## 1281               0.14252674               2
## 1282               0.08833018               4
## 1283               0.15490370               1
## 1284               0.11240423               4
## 1285               0.14453923               3
## 1286               0.13273719               2
## 1287               0.20341245               1
## 1288               0.24519554               1
## 1289               0.09033978               4
## 1290               0.24484248               2
## 1291               0.18521067               1
## 1292               0.32954700               1
## 1293               0.08833018               4
## 1294               0.28268836               3
## 1295               0.31376827               2
## 1296               0.18089314               3
## 1297               0.24115153               3
## 1298               0.11712579               2
## 1299               0.14777584               2
## 1300               0.08833018               4
## 1301               0.13044428               3
## 1302               0.17454363               2
## 1303               0.14990749               3
## 1304               0.12991915               2
## 1305               0.20757354               1
## 1306               0.08759845               4
## 1307               0.28679076               1
## 1308               0.18659103               1
## 1309               0.09971874               4
## 1310               0.08833018               4
## 1311               0.20416779               3
## 1312               0.30946407               3
## 1313               0.11272841               1
## 1314               0.33248828               1
## 1315               0.13377012               3
## 1316               0.10659476               2
## 1317               0.14518166               4
## 1318               0.09645536               4
## 1319               0.12641585               4
## 1320               0.09189219               4
## 1321               0.12779496               3
## 1322               0.11887699               3
## 1323               0.09645536               4
## 1324               0.08001127               4
## 1325               0.14327491               3
## 1326               0.12652919               3
## 1327               0.13004827               2
## 1328               0.33248828               1
## 1329               0.16173318               3
## 1330               0.14575555               2
## 1331               0.24115153               3
## 1332               0.12876347               2
## 1333               0.09645536               4
## 1334               0.12991915               2
## 1335               0.21970847               1
## 1336               0.07185564               4
## 1337               0.10453851               4
## 1338               0.14567009               2
## 1339               0.12065055               4
## 1340               0.14575555               2
## 1341               0.11887699               3
## 1342               0.14319066               3
## 1343               0.08833018               4
## 1344               0.18503844               1
## 1345               0.15490370               1
## 1346               0.11712579               2
## 1347               0.10965384               4
## 1348               0.13674006               4
## 1349               0.28679076               1
## 1350               0.15685397               3
## 1351               0.26131149               3
## 1352               0.08750724               4
## 1353               0.17455487               1
## 1354               0.15490370               1
## 1355               0.15884708               4
## 1356               0.26439301               2
## 1357               0.12991915               2
## 1358               0.23066969               1
## 1359               0.08001127               4
## 1360               0.12072341               4
## 1361               0.28268836               3
## 1362               0.08833018               4
## 1363               0.11887699               3
## 1364               0.14333080               3
## 1365               0.08001127               4
## 1366               0.18659103               1
## 1367               0.20416779               3
## 1368               0.14581224               2
## 1369               0.07254308               4
## 1370               0.11506678               3
## 1371               0.13611234               2
## 1372               0.11272841               1
## 1373               0.30896762               1
## 1374               0.12876347               2
## 1375               0.10628647               4
## 1376               0.22194381               3
## 1377               0.11489252               4
## 1378               0.11326204               4
## 1379               0.08199347               4
## 1380               0.24484248               2
## 1381               0.36186670               1
## 1382               0.15361462               3
## 1383               0.21206354               1
## 1384               0.20744743               2
## 1385               0.20691501               4
## 1386               0.12665543               3
## 1387               0.22147291               1
## 1388               0.38184110               1
## 1389               0.07254308               4
## 1390               0.18503844               1
## 1391               0.10726525               4
## 1392               0.38184110               1
## 1393               0.07254308               4
## 1394               0.08750724               4
## 1395               0.07185564               4
## 1396               0.14518166               4
## 1397               0.33274172               1
## 1398               0.26131149               3
## 1399               0.11506678               3
## 1400               0.24115153               3
## 1401               0.10659476               2
## 1402               0.10757604               2
## 1403               0.09967788               4
## 1404               0.17455487               1
## 1405               0.11506678               3
## 1406               0.16057474               3
## 1407               0.18659103               1
## 1408               0.15685397               3
## 1409               0.10113511               4
## 1410               0.15919626               3
## 1411               0.13273719               2
## 1412               0.12991915               2
## 1413               0.14127712               2
## 1414               0.17176915               3
## 1415               0.24115153               3
## 1416               0.15685397               3
## 1417               0.10659476               2
## 1418               0.22194381               3
## 1419               0.20416779               3
## 1420               0.18521067               1
## 1421               0.08750724               4
## 1422               0.31613059               2
## 1423               0.10469892               3
## 1424               0.14526667               3
## 1425               0.11887699               3
## 1426               0.09033978               4
## 1427               0.10757604               2
## 1428               0.17397810               4
## 1429               0.12099487               2
## 1430               0.19541773               4
## 1431               0.14319066               3
## 1432               0.07254308               4
## 1433               0.08833018               4
## 1434               0.26131149               3
## 1435               0.17397810               4
## 1436               0.09961629               4
## 1437               0.20938028               1
## 1438               0.10628647               4
## 1439               0.21970847               1
## 1440               0.17381408               4
## 1441               0.11712579               2
## 1442               0.12779496               3
## 1443               0.18166283               4
## 1444               0.28268836               3
## 1445               0.25853685               3
## 1446               0.20744743               2
## 1447               0.12652919               3
## 1448               0.08759845               4
## 1449               0.12991915               2
## 1450               0.18503844               1
## 1451               0.07254308               4
## 1452               0.15884708               4
## 1453               0.11887699               3
## 1454               0.09971874               4
## 1455               0.12652919               3
## 1456               0.10566481               3
## 1457               0.13377012               3
## 1458               0.10566481               3
## 1459               0.07254308               4
## 1460               0.11712579               2
## 1461               0.32954700               1
## 1462               0.18503844               1
## 1463               0.13674006               4
## 1464               0.20757354               1
## 1465               0.12652919               3
## 1466               0.08001127               4
## 1467               0.20768648               1
## 1468               0.14567009               2
## 1469               0.15489348               2
## 1470               0.17927647               3

xtabs(~ probability.of.Attrition + JobSatisfaction, data=predicted.attrition_data)

##                         JobSatisfaction
## probability.of.Attrition  1  2  3  4
##       0.0509290079067831  0  0  0  2
##       0.0514273436171294  0  0  0  4
##       0.0582998377960836  0  0  0  2
##       0.0623952334636104  0  0  0  2
##       0.0629983176993634  0  0  0  1
##       0.0713008702674125  0  0  0  1
##       0.0718556351495316  0  0  0 19
##       0.0725430845984081  0  0  0 21
##       0.0749799978493843  0  0  5  0
##       0.0756949005940833  0  0  1  0
##       0.077110782651787   0  2  0  0
##       0.0792590930438247  0  0  0 15
##       0.080011266146487   0  0  0 19
##       0.081993468100554   0  0  0 12
##       0.0855180198894394  0  0  3  0
##       0.087507237727187   0  0  0 34
##       0.0875984470468998  0  0  0 10
##       0.0883301769201772  0  0  0 35
##       0.0884221608764325  0  0  0  6
##       0.0903397835979433  0  0  0  9
##       0.0918921897522134  0  0  0  8
##       0.0927521744594639  0  0  0  3
##       0.0964553596809268  0  0  0  8
##       0.0973534712131155  0  0  0  5
##       0.098457260743169   0  1  0  0
##       0.0996162893638429  0  0  0 15
##       0.0996778826000728  0  0  0  6
##       0.0997187407399155  0  0  0 11
##       0.100602658695497   0  0  0  9
##       0.101135113194539   0  0  0  3
##       0.102071876199039   0  0  0  3
##       0.103918975399478   0  0  1  0
##       0.104538506138376   0  0  0  2
##       0.10469891785967    0  0 23  0
##       0.105323474886705   0  0  0  2
##       0.105664810160256   0  0 25  0
##       0.106286467128127   0  0  0 13
##       0.106594757383462   0 12  0  0
##       0.107265250546574   0  0  0 15
##       0.107576038089765   0 18  0  0
##       0.109653835581753   0  0  0  4
##       0.111384399895774   0  0  0  6
##       0.112404225208671   0  0  0  6
##       0.112728407991961   3  0  0  0
##       0.11326203772172    0  0  0  7
##       0.113758963576751   1  0  0  0
##       0.114892517602362   0  0  0  3
##       0.115066775691243   0  0 16  0
##       0.116115910875028   0  0 12  0
##       0.117125791387022   0 15  0  0
##       0.118191192539639   0  5  0  0
##       0.118876992593182   0  0 16  0
##       0.120650553018122   0  0  0 10
##       0.120723408053277   0  0  0  7
##       0.120994866523147   0 12  0  0
##       0.121817018613995   0  0  0  6
##       0.125797497861938   0  0  0  1
##       0.126340050931888   0  0  0  2
##       0.126415847673817   0  0  0  2
##       0.126529189520492   0  0 31  0
##       0.126655426204567   0  0  9  0
##       0.127667757177992   0  0 29  0
##       0.127794963602211   0  0  7  0
##       0.127838558252525   5  0  0  0
##       0.128763469974754   0 18  0  0
##       0.128891606840147   0  1  0  0
##       0.129919152303181   0 23  0  0
##       0.130048267559357   0  4  0  0
##       0.130444281026318   0  0 10  0
##       0.132585399361209   0  0  4  0
##       0.132737189137561   0  8  0  0
##       0.133770117545264   0  0  6  0
##       0.13611233527977    0  2  0  0
##       0.136740055060516   0  0  0  6
##       0.138860312712789   0  0  7  0
##       0.140092044919744   0  0  1  0
##       0.141277120194971   0  4  0  0
##       0.142413348775066   1  0  0  0
##       0.142526742043798   0  5  0  0
##       0.14306484214723    0  0  0  2
##       0.143190664405774   0  0 18  0
##       0.143274912664277   0  0 12  0
##       0.14333079632972    0  0  5  0
##       0.144539231016402   0  0 12  0
##       0.145181658301975   0  0  0 20
##       0.145266667381274   0  0  5  0
##       0.145670090677133   0 16  0  0
##       0.145755549577505   0  9  0  0
##       0.145812236126969   0  3  0  0
##       0.14654555537306    0  0  2  0
##       0.147038001148758   0  3  0  0
##       0.147775840916641   0  3  0  0
##       0.149072966283064   0  2  0  0
##       0.149907494334225   0  0  3  0
##       0.150975696617432   0  0  3  0
##       0.152285047846937   0  0  5  0
##       0.15356576449936    0  1  0  0
##       0.153614619077793   0  0 14  0
##       0.153814012517148   2  0  0  0
##       0.154893480328818   0 16  0  0
##       0.154903696838202  16  0  0  0
##       0.156241627873186   0  7  0  0
##       0.156251916863363  13  0  0  0
##       0.156853970839863   0  0  9  0
##       0.158847080347473   0  0  0 13
##       0.159196257994002   0  0  2  0
##       0.159525935547074   0  1  0  0
##       0.160574739934627   0  0 11  0
##       0.16173318099462    0  0  8  0
##       0.161900461305183   0  5  0  0
##       0.163297811252923   0  5  0  0
##       0.16447204832165    0  3  0  0
##       0.169302976820758   8  0  0  0
##       0.1707512004779     9  0  0  0
##       0.171671502508262   0  0  3  0
##       0.171769148485401   0  0  4  0
##       0.17323406854789    0  0  4  0
##       0.173380866518913   0  0  0  2
##       0.173814080718024   0  0  0 12
##       0.173978096540129   0  0  0  9
##       0.174543626710983   0  8  0  0
##       0.174554871605932   6  0  0  0
##       0.176126776416665   0  2  0  0
##       0.178553046391665   0  0  1  0
##       0.179276468779857   0  0  2  0
##       0.180678461133255   0  0  1  0
##       0.180893139056416   0  0  1  0
##       0.181662834254414   0  0  0  5
##       0.182247832910883   0  3  0  0
##       0.182350170331644   0  1  0  0
##       0.183885294709649   0  1  0  0
##       0.185038437559028  29  0  0  0
##       0.185210670616467   3  0  0  0
##       0.186591028695308  26  0  0  0
##       0.186764375715122   6  0  0  0
##       0.18754462338252    0  0  0  2
##       0.189113363320436   0  0  0  3
##       0.189752345724027   0  0  0  3
##       0.190369363648409  10  0  0  0
##       0.191681283849845   0  1  0  0
##       0.193071079336448   0  0  2  0
##       0.193275468107813   2  0  0  0
##       0.194880646083123   2  0  0  0
##       0.195417729603417   0  0  0  7
##       0.197966855825351   0  0  0  1
##       0.201393549310678   0  0  2  0
##       0.201754603760539   1  0  0  0
##       0.203412445852437   6  0  0  0
##       0.204167785672997   0  0 12  0
##       0.204558013968573   0  0  0  3
##       0.206232940501757   0  0  0  6
##       0.206915006914568   0  0  0  5
##       0.207447425736185   0  9  0  0
##       0.207573535534971   7  0  0  0
##       0.207686482298745   4  0  0  0
##       0.207761396785367   2  0  0  0
##       0.209380282045724  11  0  0  0
##       0.210306176177526   0  0  0  2
##       0.210353806698662   1  0  0  0
##       0.212063537618124   3  0  0  0
##       0.215674730376081   0  0  0  1
##       0.216547168400016   3  0  0  0
##       0.217968471836822   1  0  0  0
##       0.219708474225798   8  0  0  0
##       0.221472913544375   9  0  0  0
##       0.221943805378288   0  0 10  0
##       0.225428106217822   0  5  0  0
##       0.225761539047481   2  0  0  0
##       0.228802914405725   0  0  0  1
##       0.228853520077302   1  0  0  0
##       0.228924075570263   0  0  0  1
##       0.230669690636481   2  0  0  0
##       0.231480121342915   0  0  0  2
##       0.232193941700538   4  0  0  0
##       0.238729264406724   0  0  1  0
##       0.240599355719945   0  0  1  0
##       0.240963833619512   0  0  0  1
##       0.241151526282332   0  0 21  0
##       0.241360520697161   0  0  6  0
##       0.244284577496501   0  2  0  0
##       0.244842478735896   0 13  0  0
##       0.24505363894791    0  2  0  0
##       0.245195537324504   7  0  0  0
##       0.245322617743932   1  0  0  0
##       0.247227584838395   2  0  0  0
##       0.251116762211551   0  0  6  0
##       0.25490900297663    0  1  0  0
##       0.255185142811261   1  0  0  0
##       0.257140599498429   3  0  0  0
##       0.258536851336972   0  0  1  0
##       0.260509008561369   0  0  1  0
##       0.26131148629305    0  0  6  0
##       0.262401883726328   0  1  0  0
##       0.264393010843622   0  1  0  0
##       0.265203162169218   0  2  0  0
##       0.268405639768603   0  0  6  0
##       0.269604466715346   0  1  0  0
##       0.271585479947482   0  0  1  0
##       0.27236401254192    0  3  0  0
##       0.272742423350016   1  0  0  0
##       0.27557308381707    0  1  0  0
##       0.279772707428973   0  0  4  0
##       0.28184527909725    0  0  1  0
##       0.282688356682348   0  0 13  0
##       0.283293487042157   3  0  0  0
##       0.283833680613878   0  2  0  0
##       0.285924393126101   0  2  0  0
##       0.286774800045495   0  2  0  0
##       0.286790763289162   9  0  0  0
##       0.286872186706422   0  0  1  0
##       0.293468918441472   0  0  2  0
##       0.297646536419118   0  3  0  0
##       0.308967615390497   6  0  0  0
##       0.309464071629478   0  0  1  0
##       0.312702396008166   0  0  4  0
##       0.312922647133924   0  0  0  2
##       0.313768266405902   0  4  0  0
##       0.316130592218064   0  2  0  0
##       0.317030952739893   0  1  0  0
##       0.329546998836545   5  0  0  0
##       0.331818422000885   1  0  0  0
##       0.332488280563482  14  0  0  0
##       0.332741723118045   2  0  0  0
##       0.35669476567226    1  0  0  0
##       0.360678321003082   0  0  0  1
##       0.361866697123994   2  0  0  0
##       0.368846380965801   3  0  0  0
##       0.37844232476821    2  0  0  0
##       0.381841095606331   7  0  0  0
##       0.38670128793995    1  0  0  0
##       0.394324269994077   4  0  0  0
##       0.407566651971291   0  0  3  0
##       0.412772631671937   1  0  0  0
##       0.41627323221199    1  0  0  0
##       0.433407445425862   0  0  1  0
##       0.438341225640952   0  1  0  0
##       0.460093985847148   0  0  4  0
##       0.465082193165234   0  1  0  0
##       0.495921480786214   0  0  1  0
##       0.500937723556929   0  1  0  0
##       0.518838682201947   2  0  0  0
##       0.545241455977253   1  0  0  0
##       0.571863931081163   2  0  0  0

logistic <- glm(Attrition ~ ., data=attrition_data, family="binomial")
summary(logistic)

## 
## Call:
## glm(formula = Attrition ~ ., family = "binomial", data = attrition_data)
## 
## Coefficients:
##                                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                       2.081e+00  7.034e-01   2.959 0.003086 ** 
## DepartmentResearch & Development -1.083e-01  5.367e-01  -0.202 0.840158    
## DepartmentSales                   3.994e-01  5.521e-01   0.723 0.469419    
## MaritalStatusMarried              2.797e-01  2.305e-01   1.214 0.224852    
## MaritalStatusSingle               1.152e+00  2.283e-01   5.046 4.52e-07 ***
## EducationFieldLife Sciences      -1.050e+00  7.253e-01  -1.447 0.147857    
## EducationFieldMarketing          -6.236e-01  7.643e-01  -0.816 0.414508    
## EducationFieldMedical            -1.195e+00  7.282e-01  -1.641 0.100808    
## EducationFieldOther              -1.094e+00  7.900e-01  -1.385 0.166159    
## EducationFieldTechnical Degree   -4.425e-01  7.411e-01  -0.597 0.550448    
## Education2                       -7.608e-03  2.866e-01  -0.027 0.978824    
## Education3                        1.119e-02  2.531e-01   0.044 0.964723    
## Education4                       -7.320e-02  2.794e-01  -0.262 0.793309    
## Education5                       -3.277e-01  5.462e-01  -0.600 0.548546    
## DistanceFromHome                  3.262e-02  9.159e-03   3.561 0.000369 ***
## EnvironmentSatisfaction2         -6.947e-01  2.330e-01  -2.982 0.002867 ** 
## EnvironmentSatisfaction3         -8.730e-01  2.132e-01  -4.094 4.24e-05 ***
## EnvironmentSatisfaction4         -8.957e-01  2.146e-01  -4.174 2.99e-05 ***
## JobSatisfaction2                 -5.291e-01  2.353e-01  -2.249 0.024538 *  
## JobSatisfaction3                 -4.733e-01  2.081e-01  -2.275 0.022913 *  
## JobSatisfaction4                 -9.747e-01  2.213e-01  -4.404 1.06e-05 ***
## Age                              -3.526e-02  1.085e-02  -3.249 0.001159 ** 
## MonthlyIncome                    -1.042e-04  2.882e-05  -3.616 0.000300 ***
## NumCompaniesWorked                1.115e-01  3.224e-02   3.458 0.000544 ***
## WorkLifeBalance2                 -7.698e-01  3.114e-01  -2.472 0.013439 *  
## WorkLifeBalance3                 -1.082e+00  2.877e-01  -3.762 0.000169 ***
## WorkLifeBalance4                 -7.668e-01  3.549e-01  -2.161 0.030715 *  
## YearsAtCompany                   -2.176e-02  1.951e-02  -1.116 0.264531    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1298.6  on 1469  degrees of freedom
## Residual deviance: 1095.2  on 1442  degrees of freedom
## AIC: 1151.2
## 
## Number of Fisher Scoring iterations: 5

## Now calculate the overall "Pseudo R-squared" and its p-value
ll.null <- logistic$null.deviance/-2
ll.proposed <- logistic$deviance/-2
(ll.null - ll.proposed) / ll.null

## [1] 0.1566413

## The p-value for the R^2
1 - pchisq(2*(ll.proposed - ll.null), df=(length(logistic$coefficients)-1))

## [1] 0

predicted.attrition_data <- data.frame(probability.of.Attrition=logistic$fitted.values,Attrition=attrition_data$Attrition)
predicted.attrition_data <- predicted.attrition_data[order(predicted.attrition_data$probability.of.Attrition, decreasing=FALSE),]
predicted.attrition_data$rank <- 1:nrow(predicted.attrition_data)

# The Pseudo R-squared measures the proportion of total variance in the response variable that is explained by the model.
# The output of 0.2 indicates that the model does not fits the data perfectly.

# As the p-value for R^2 is less than 0.05, we reject the null hypothesis.

plot(logistic)

# Residuals vs Fitted are a great way to identify heteroscedasticity via pattern recognition, however our model does not seem to have any.
# Q-Q Plots are great in understanding the distribution of residuals. As it can be observed that there is quite some deviation from the straight line indicating that residuals do not follow a normal distribution.
# Scale-Location Plot shows the square root of the standardized residuals against the fitted values. As it may be observed that the spread of points is not consistent across the range of fitted values, it indicates that the variability of the residuals do not remain constant.
# Residuals Vs Leverage help in identifying potential problems with the regression model. Points on the right of the plot have a great influence on the model's parameters. Points with a Cook's Distance greater than highlighted threshold have a greater influence on the model.

ggplot(data=predicted.attrition_data, aes(x=rank, y=probability.of.Attrition)) +
geom_point(aes(color=Attrition), alpha=1, shape=4, stroke=2) +
xlab("Index") +
ylab("Predicted probability of Attrition")

# This plot highlights the performace of our model.
# It can be clearly inferred that the model performs poorly.

# From Caret
pdata <- predict(logistic,newdata=attrition_data,type="response" )
pdata

##           1           2           3           4           5           6 
## 0.408492594 0.032649514 0.228672082 0.059930466 0.301137938 0.108368355 
##           7           8           9          10          11          12 
## 0.082374800 0.119863740 0.105012483 0.187685441 0.165726881 0.175172192 
##          13          14          15          16          17          18 
## 0.296189944 0.053094561 0.428664934 0.082384687 0.139115721 0.087880197 
##          19          20          21          22          23          24 
## 0.015495948 0.113102159 0.203580914 0.473883971 0.110025185 0.244133387 
##          25          26          27          28          29          30 
## 0.264553173 0.008327191 0.305253338 0.072575521 0.026398205 0.145700592 
##          31          32          33          34          35          36 
## 0.127543427 0.035073559 0.163975540 0.193892777 0.095917807 0.043424939 
##          37          38          39          40          41          42 
## 0.209999348 0.107605383 0.307334036 0.140607893 0.036419116 0.102597279 
##          43          44          45          46          47          48 
## 0.644033005 0.176304832 0.069126258 0.020096006 0.392977382 0.156280961 
##          49          50          51          52          53          54 
## 0.282663362 0.053687109 0.325927834 0.349431255 0.174793881 0.064501850 
##          55          56          57          58          59          60 
## 0.417620313 0.060807986 0.147049886 0.170520433 0.043560479 0.088887818 
##          61          62          63          64          65          66 
## 0.056778525 0.123927652 0.009147970 0.521737381 0.038951666 0.008461105 
##          67          68          69          70          71          72 
## 0.138691420 0.046852899 0.190759758 0.081620697 0.357831981 0.068003759 
##          73          74          75          76          77          78 
## 0.134856545 0.050131943 0.068187639 0.087171911 0.269626516 0.052051514 
##          79          80          81          82          83          84 
## 0.175635763 0.068843818 0.042998971 0.138553093 0.046765229 0.040527797 
##          85          86          87          88          89          90 
## 0.101983405 0.060594949 0.361177512 0.035698745 0.036659502 0.051423682 
##          91          92          93          94          95          96 
## 0.014859223 0.307933405 0.076429002 0.036612310 0.187217492 0.255271578 
##          97          98          99         100         101         102 
## 0.285200076 0.160811997 0.023113873 0.174347534 0.290812115 0.228568070 
##         103         104         105         106         107         108 
## 0.169300905 0.207768713 0.050187664 0.024535768 0.027969995 0.322085585 
##         109         110         111         112         113         114 
## 0.058353621 0.216796791 0.196718820 0.239273035 0.079032956 0.153928768 
##         115         116         117         118         119         120 
## 0.078743592 0.099551556 0.092960489 0.071592030 0.111806198 0.022328250 
##         121         122         123         124         125         126 
## 0.269992245 0.217792142 0.089748993 0.059408490 0.175489165 0.122709904 
##         127         128         129         130         131         132 
## 0.008291107 0.701580372 0.105593171 0.067043063 0.264053071 0.137251795 
##         133         134         135         136         137         138 
## 0.239917367 0.053946622 0.169708093 0.074435612 0.071370097 0.096348346 
##         139         140         141         142         143         144 
## 0.372251360 0.242208371 0.639596441 0.222699094 0.179607855 0.525274180 
##         145         146         147         148         149         150 
## 0.054452384 0.236381021 0.099188010 0.033988481 0.109438004 0.266445447 
##         151         152         153         154         155         156 
## 0.048017431 0.060481776 0.292825953 0.213286787 0.165114568 0.100918714 
##         157         158         159         160         161         162 
## 0.036495892 0.069088231 0.079742338 0.240635964 0.099546520 0.293259135 
##         163         164         165         166         167         168 
## 0.204044730 0.051319938 0.086373404 0.025270515 0.165850767 0.052128591 
##         169         170         171         172         173         174 
## 0.236464640 0.153905326 0.235856163 0.661697693 0.199504713 0.083173107 
##         175         176         177         178         179         180 
## 0.135033081 0.058664172 0.124333994 0.272415949 0.046670105 0.111169431 
##         181         182         183         184         185         186 
## 0.101703703 0.271737638 0.477948942 0.047225123 0.043457997 0.076223514 
##         187         188         189         190         191         192 
## 0.006824491 0.024331133 0.040298496 0.028886522 0.002727602 0.233236339 
##         193         194         195         196         197         198 
## 0.136765101 0.046688133 0.023894715 0.213497357 0.172532214 0.052723048 
##         199         200         201         202         203         204 
## 0.091355067 0.286310356 0.269270779 0.018111284 0.063060600 0.129969309 
##         205         206         207         208         209         210 
## 0.259242503 0.208270044 0.109991017 0.142982369 0.156832319 0.041164175 
##         211         212         213         214         215         216 
## 0.031590470 0.084007856 0.224880457 0.069591120 0.481932775 0.062283301 
##         217         218         219         220         221         222 
## 0.692613582 0.319234127 0.071558117 0.103146660 0.224898959 0.099528991 
##         223         224         225         226         227         228 
## 0.015024796 0.076093985 0.044533926 0.026279814 0.184188605 0.041923375 
##         229         230         231         232         233         234 
## 0.211442273 0.206293750 0.130439607 0.007775105 0.113844970 0.006628429 
##         235         236         237         238         239         240 
## 0.215678497 0.036074117 0.409199673 0.043433756 0.113779511 0.303215643 
##         241         242         243         244         245         246 
## 0.070196131 0.157462579 0.158161648 0.169119814 0.002908839 0.047170223 
##         247         248         249         250         251         252 
## 0.061597600 0.102217020 0.107597451 0.111668426 0.104835892 0.064029845 
##         253         254         255         256         257         258 
## 0.162536656 0.222815597 0.115277538 0.143378429 0.044344284 0.009829489 
##         259         260         261         262         263         264 
## 0.033472691 0.296307649 0.231825947 0.051625846 0.432966495 0.048541911 
##         265         266         267         268         269         270 
## 0.614601253 0.188262316 0.057158009 0.117593710 0.009417524 0.030092747 
##         271         272         273         274         275         276 
## 0.008913491 0.097855453 0.077408756 0.070983879 0.241171971 0.019315141 
##         277         278         279         280         281         282 
## 0.099967987 0.173307397 0.115336863 0.020112101 0.010887560 0.056101556 
##         283         284         285         286         287         288 
## 0.197541283 0.063957348 0.253242651 0.068063552 0.227962665 0.088589867 
##         289         290         291         292         293         294 
## 0.199255607 0.124191582 0.086165931 0.239119437 0.185571464 0.186507812 
##         295         296         297         298         299         300 
## 0.069179774 0.125530093 0.285953799 0.140475644 0.079993508 0.027877388 
##         301         302         303         304         305         306 
## 0.031874492 0.419634385 0.252791454 0.193860205 0.010310030 0.158501737 
##         307         308         309         310         311         312 
## 0.113066413 0.111030700 0.016477763 0.060995615 0.471313424 0.078728003 
##         313         314         315         316         317         318 
## 0.087085823 0.040542810 0.016783049 0.072587849 0.093159672 0.038197955 
##         319         320         321         322         323         324 
## 0.248244764 0.147091095 0.230128332 0.080031035 0.299548325 0.174954917 
##         325         326         327         328         329         330 
## 0.059808637 0.041656003 0.004585408 0.121319039 0.363052092 0.009989507 
##         331         332         333         334         335         336 
## 0.043723996 0.115341029 0.161337208 0.131609074 0.057744309 0.052134877 
##         337         338         339         340         341         342 
## 0.197474419 0.094715169 0.097852915 0.161969938 0.046400010 0.013340553 
##         343         344         345         346         347         348 
## 0.076026098 0.095461857 0.105495098 0.126162587 0.131919108 0.211676595 
##         349         350         351         352         353         354 
## 0.075501240 0.137737610 0.072317041 0.057975772 0.349078571 0.068894444 
##         355         356         357         358         359         360 
## 0.543736169 0.099288951 0.129153319 0.666145547 0.087196098 0.070184028 
##         361         362         363         364         365         366 
## 0.018162322 0.079143039 0.503227775 0.345534384 0.159178485 0.053710721 
##         367         368         369         370         371         372 
## 0.280173860 0.099077864 0.172981224 0.167713636 0.393574254 0.394216374 
##         373         374         375         376         377         378 
## 0.245552379 0.045178904 0.178926388 0.112374765 0.077496110 0.090824146 
##         379         380         381         382         383         384 
## 0.716453324 0.012880788 0.211938896 0.209615484 0.366957219 0.245056032 
##         385         386         387         388         389         390 
## 0.057639518 0.396525043 0.101982703 0.127119330 0.081824179 0.200322398 
##         391         392         393         394         395         396 
## 0.023478141 0.096338869 0.042130216 0.235674296 0.244256903 0.096638807 
##         397         398         399         400         401         402 
## 0.046892066 0.199089944 0.081550398 0.114099865 0.006592622 0.097481934 
##         403         404         405         406         407         408 
## 0.375362185 0.116850315 0.099870357 0.331135768 0.021161859 0.142424167 
##         409         410         411         412         413         414 
## 0.018182756 0.177203510 0.086563420 0.058107089 0.054284628 0.112067992 
##         415         416         417         418         419         420 
## 0.606917844 0.170643922 0.042313938 0.011529497 0.386671824 0.186210497 
##         421         422         423         424         425         426 
## 0.028192698 0.344124446 0.564529758 0.144980639 0.109215599 0.013370111 
##         427         428         429         430         431         432 
## 0.101983290 0.153184891 0.049350421 0.111716539 0.192994265 0.153859290 
##         433         434         435         436         437         438 
## 0.055151885 0.053894921 0.034689881 0.087739873 0.144537701 0.331045866 
##         439         440         441         442         443         444 
## 0.077802330 0.183480375 0.442290803 0.096872179 0.103033425 0.429719853 
##         445         446         447         448         449         450 
## 0.049038492 0.087421391 0.158412544 0.262830068 0.082230263 0.057675223 
##         451         452         453         454         455         456 
## 0.222451990 0.102234999 0.062376403 0.144345021 0.173385540 0.026412491 
##         457         458         459         460         461         462 
## 0.087081332 0.539555645 0.132297941 0.162636714 0.465155177 0.307536808 
##         463         464         465         466         467         468 
## 0.165361157 0.635977086 0.185479715 0.141442914 0.042498550 0.082052793 
##         469         470         471         472         473         474 
## 0.071948309 0.211971853 0.150194811 0.043761305 0.093703638 0.004787429 
##         475         476         477         478         479         480 
## 0.110880387 0.544583589 0.144378543 0.010144281 0.197571389 0.217728320 
##         481         482         483         484         485         486 
## 0.351485453 0.042336244 0.393000222 0.388190983 0.154233951 0.163645694 
##         487         488         489         490         491         492 
## 0.135850314 0.272238149 0.023023580 0.013896009 0.307226508 0.025211333 
##         493         494         495         496         497         498 
## 0.089844353 0.295317973 0.189585331 0.199590115 0.604888907 0.009603225 
##         499         500         501         502         503         504 
## 0.196196588 0.083450655 0.106469490 0.061425710 0.188688781 0.042424864 
##         505         506         507         508         509         510 
## 0.394414351 0.064915414 0.027804267 0.129735410 0.060725265 0.066951560 
##         511         512         513         514         515         516 
## 0.030740570 0.036419582 0.205168278 0.285874856 0.373720708 0.083614094 
##         517         518         519         520         521         522 
## 0.374147324 0.121707105 0.154423551 0.036231967 0.086931534 0.046336473 
##         523         524         525         526         527         528 
## 0.115251709 0.052022486 0.107501664 0.680161620 0.124564313 0.251519185 
##         529         530         531         532         533         534 
## 0.129795329 0.060958850 0.073385208 0.053495793 0.334298169 0.074917220 
##         535         536         537         538         539         540 
## 0.015176858 0.024897146 0.632982499 0.085002374 0.020656210 0.166245615 
##         541         542         543         544         545         546 
## 0.474779056 0.219664469 0.150756424 0.341839702 0.035173942 0.229374470 
##         547         548         549         550         551         552 
## 0.328244596 0.103156911 0.064423354 0.157101552 0.239163210 0.464114819 
##         553         554         555         556         557         558 
## 0.021375960 0.084214965 0.587025042 0.181455685 0.068184850 0.090241085 
##         559         560         561         562         563         564 
## 0.126537107 0.170077366 0.089618739 0.024201514 0.099821613 0.293937119 
##         565         566         567         568         569         570 
## 0.189358946 0.399522944 0.314154848 0.098949223 0.012083599 0.382856406 
##         571         572         573         574         575         576 
## 0.023830889 0.100735318 0.233129772 0.712374508 0.107031833 0.096698879 
##         577         578         579         580         581         582 
## 0.116733076 0.107231148 0.346316744 0.153491383 0.213822474 0.085445728 
##         583         584         585         586         587         588 
## 0.036118229 0.201787729 0.006331127 0.195994107 0.091672321 0.087770058 
##         589         590         591         592         593         594 
## 0.011832989 0.151453725 0.029870175 0.774470790 0.005177597 0.035861016 
##         595         596         597         598         599         600 
## 0.130916009 0.012317928 0.165120748 0.051134256 0.266488218 0.300759558 
##         601         602         603         604         605         606 
## 0.045332361 0.384422802 0.138478252 0.137970975 0.134602314 0.213644751 
##         607         608         609         610         611         612 
## 0.133773926 0.061946709 0.087742454 0.054831018 0.026409102 0.121195815 
##         613         614         615         616         617         618 
## 0.151219262 0.259208825 0.080085590 0.076437142 0.114923918 0.198130802 
##         619         620         621         622         623         624 
## 0.663858072 0.194454005 0.412903455 0.052189156 0.106177227 0.121192969 
##         625         626         627         628         629         630 
## 0.115469235 0.100922513 0.116700253 0.013848714 0.156306749 0.042658715 
##         631         632         633         634         635         636 
## 0.215811021 0.114945130 0.120748177 0.245832420 0.181435118 0.027940883 
##         637         638         639         640         641         642 
## 0.111053441 0.031672297 0.332940332 0.112441059 0.155047203 0.086745760 
##         643         644         645         646         647         648 
## 0.175087084 0.038520004 0.069226706 0.163641599 0.096538155 0.100757466 
##         649         650         651         652         653         654 
## 0.135518481 0.041142106 0.041012237 0.046624612 0.316801972 0.012608905 
##         655         656         657         658         659         660 
## 0.063020605 0.236211585 0.625516966 0.147404747 0.102605742 0.268249716 
##         661         662         663         664         665         666 
## 0.049116375 0.155911098 0.388846799 0.278227832 0.036908665 0.117180933 
##         667         668         669         670         671         672 
## 0.129038337 0.049013173 0.112366548 0.372872170 0.242892135 0.085990577 
##         673         674         675         676         677         678 
## 0.268604412 0.240378313 0.021212257 0.227477355 0.149191329 0.075449303 
##         679         680         681         682         683         684 
## 0.120896199 0.221462196 0.097117518 0.043358233 0.118669051 0.314608345 
##         685         686         687         688         689         690 
## 0.196322723 0.293457942 0.124853461 0.138041650 0.560256379 0.693559538 
##         691         692         693         694         695         696 
## 0.090368485 0.081225404 0.079503107 0.024050170 0.067307864 0.276766461 
##         697         698         699         700         701         702 
## 0.048315228 0.240556839 0.121779412 0.006690702 0.172013603 0.020089269 
##         703         704         705         706         707         708 
## 0.129612673 0.209173008 0.043317467 0.167254348 0.273364461 0.033128054 
##         709         710         711         712         713         714 
## 0.208162934 0.242442726 0.083954612 0.457797560 0.181493974 0.021609633 
##         715         716         717         718         719         720 
## 0.010785726 0.042268886 0.021983079 0.375071365 0.110866407 0.081507396 
##         721         722         723         724         725         726 
## 0.362038786 0.026600791 0.083528340 0.023900072 0.083435336 0.149407960 
##         727         728         729         730         731         732 
## 0.097939367 0.239877445 0.083061216 0.041123078 0.080944152 0.362581356 
##         733         734         735         736         737         738 
## 0.171215367 0.032711224 0.267526509 0.226527398 0.064137831 0.162195548 
##         739         740         741         742         743         744 
## 0.008448412 0.089516936 0.056315964 0.070138047 0.105650462 0.016906522 
##         745         746         747         748         749         750 
## 0.404442161 0.033667422 0.006889242 0.209399321 0.733592218 0.012852644 
##         751         752         753         754         755         756 
## 0.034593303 0.028951560 0.223608001 0.102163121 0.259923040 0.020581033 
##         757         758         759         760         761         762 
## 0.409285955 0.040642771 0.079916900 0.199295665 0.046198239 0.293584503 
##         763         764         765         766         767         768 
## 0.418577429 0.141213637 0.164846968 0.069921881 0.009885763 0.176603662 
##         769         770         771         772         773         774 
## 0.274271084 0.133766634 0.007228760 0.036606027 0.086271384 0.041347440 
##         775         776         777         778         779         780 
## 0.060354464 0.051011883 0.373314182 0.492922359 0.081211009 0.222905253 
##         781         782         783         784         785         786 
## 0.497740116 0.209881068 0.114419490 0.106894586 0.046029607 0.124879350 
##         787         788         789         790         791         792 
## 0.141058247 0.017081585 0.278316311 0.065284308 0.032936580 0.258723043 
##         793         794         795         796         797         798 
## 0.364127468 0.262894777 0.153311857 0.044380967 0.118837237 0.300750063 
##         799         800         801         802         803         804 
## 0.535740605 0.009350620 0.123738097 0.133067383 0.096750189 0.053303404 
##         805         806         807         808         809         810 
## 0.039437410 0.062762114 0.083857447 0.060471938 0.103641011 0.035973284 
##         811         812         813         814         815         816 
## 0.063598895 0.312709664 0.143540721 0.035174498 0.029472060 0.409856027 
##         817         818         819         820         821         822 
## 0.273077941 0.173081671 0.120991782 0.333931050 0.076314896 0.067659233 
##         823         824         825         826         827         828 
## 0.187374390 0.079313991 0.203208789 0.058628602 0.200136134 0.074402466 
##         829         830         831         832         833         834 
## 0.277075894 0.504479877 0.054169873 0.135280899 0.069389924 0.096795322 
##         835         836         837         838         839         840 
## 0.148437516 0.487587794 0.413453788 0.119961471 0.116222640 0.558866540 
##         841         842         843         844         845         846 
## 0.082517180 0.450382568 0.101313548 0.082076642 0.141392703 0.181215732 
##         847         848         849         850         851         852 
## 0.032197837 0.114817384 0.055471084 0.690451684 0.142815676 0.016212419 
##         853         854         855         856         857         858 
## 0.049590362 0.391762350 0.165410692 0.027497445 0.497020298 0.121686115 
##         859         860         861         862         863         864 
## 0.006194479 0.108688872 0.058681795 0.056551631 0.201462756 0.206061677 
##         865         866         867         868         869         870 
## 0.515168333 0.417438066 0.113807334 0.013547894 0.152769246 0.018667747 
##         871         872         873         874         875         876 
## 0.148116866 0.340362715 0.216093985 0.048408835 0.071400523 0.083392426 
##         877         878         879         880         881         882 
## 0.464822611 0.031793144 0.099736015 0.025620108 0.096529158 0.155069865 
##         883         884         885         886         887         888 
## 0.066121512 0.079256959 0.255798355 0.171056103 0.044127677 0.114363410 
##         889         890         891         892         893         894 
## 0.084719067 0.408961768 0.056622367 0.065635294 0.549249360 0.078866134 
##         895         896         897         898         899         900 
## 0.005065190 0.113236345 0.242297591 0.080904594 0.006492971 0.028311368 
##         901         902         903         904         905         906 
## 0.115611484 0.293609127 0.151757902 0.029347495 0.030279770 0.014867424 
##         907         908         909         910         911         912 
## 0.243720100 0.041382943 0.055811465 0.322625656 0.111871493 0.384074926 
##         913         914         915         916         917         918 
## 0.154701096 0.085234121 0.004369332 0.726044311 0.020967553 0.352827145 
##         919         920         921         922         923         924 
## 0.010874390 0.052204159 0.098379017 0.175363751 0.010148211 0.127192288 
##         925         926         927         928         929         930 
## 0.063303150 0.102100577 0.093156046 0.168717028 0.047986394 0.047636978 
##         931         932         933         934         935         936 
## 0.112445864 0.239907778 0.158622214 0.503633142 0.222243748 0.065468989 
##         937         938         939         940         941         942 
## 0.063954318 0.013933762 0.101606251 0.058929933 0.239670293 0.144847678 
##         943         944         945         946         947         948 
## 0.098459820 0.285793387 0.027610246 0.047804484 0.269033835 0.245891192 
##         949         950         951         952         953         954 
## 0.067754508 0.284496270 0.050136937 0.107495098 0.299137154 0.294910619 
##         955         956         957         958         959         960 
## 0.009707200 0.005261863 0.025380178 0.135370163 0.024303038 0.059609266 
##         961         962         963         964         965         966 
## 0.106841334 0.113347347 0.005795469 0.103005924 0.339921171 0.123741153 
##         967         968         969         970         971         972 
## 0.049490377 0.072076673 0.437857587 0.033663570 0.207425828 0.108813279 
##         973         974         975         976         977         978 
## 0.229879734 0.021044761 0.170684089 0.270080827 0.020209337 0.357878363 
##         979         980         981         982         983         984 
## 0.039712846 0.150827100 0.359015222 0.215824333 0.053367025 0.116219595 
##         985         986         987         988         989         990 
## 0.296899001 0.092807596 0.230353379 0.054203337 0.057344766 0.112849622 
##         991         992         993         994         995         996 
## 0.099060430 0.169594092 0.061412076 0.421032103 0.036431173 0.353984819 
##         997         998         999        1000        1001        1002 
## 0.113977353 0.238931429 0.186614964 0.051002925 0.315855756 0.364114719 
##        1003        1004        1005        1006        1007        1008 
## 0.090697216 0.325665649 0.244834300 0.327299292 0.493027915 0.081234151 
##        1009        1010        1011        1012        1013        1014 
## 0.015637178 0.007878551 0.006044417 0.357087948 0.298887904 0.308652160 
##        1015        1016        1017        1018        1019        1020 
## 0.139157041 0.101563451 0.479242424 0.235194954 0.168994602 0.369440080 
##        1021        1022        1023        1024        1025        1026 
## 0.221945948 0.460993178 0.423560162 0.172081627 0.023261516 0.115826379 
##        1027        1028        1029        1030        1031        1032 
## 0.088553643 0.114942193 0.070689757 0.064290873 0.059430025 0.123447734 
##        1033        1034        1035        1036        1037        1038 
## 0.457898108 0.064224844 0.048240355 0.356621948 0.223485677 0.135585915 
##        1039        1040        1041        1042        1043        1044 
## 0.151819565 0.302950183 0.013589228 0.206891812 0.137755106 0.028295652 
##        1045        1046        1047        1048        1049        1050 
## 0.167118435 0.059763001 0.204105277 0.132471106 0.274253727 0.338923079 
##        1051        1052        1053        1054        1055        1056 
## 0.135380111 0.333765763 0.190469995 0.029559300 0.016893829 0.064082077 
##        1057        1058        1059        1060        1061        1062 
## 0.525059081 0.872322031 0.461800884 0.129316388 0.454257809 0.206166747 
##        1063        1064        1065        1066        1067        1068 
## 0.114675877 0.083673285 0.081708627 0.026188292 0.218103656 0.119945163 
##        1069        1070        1071        1072        1073        1074 
## 0.467827238 0.362025901 0.327995570 0.065782711 0.065508126 0.147378083 
##        1075        1076        1077        1078        1079        1080 
## 0.114178899 0.073586862 0.005310038 0.863695062 0.052717346 0.133640523 
##        1081        1082        1083        1084        1085        1086 
## 0.043417005 0.254438103 0.509376618 0.501250334 0.105975270 0.322130476 
##        1087        1088        1089        1090        1091        1092 
## 0.011435312 0.199353702 0.051597185 0.081566315 0.084082898 0.228643049 
##        1093        1094        1095        1096        1097        1098 
## 0.155812916 0.034254307 0.255343266 0.106387134 0.015185339 0.298471039 
##        1099        1100        1101        1102        1103        1104 
## 0.034912244 0.069812487 0.214915014 0.062554819 0.211128336 0.100244086 
##        1105        1106        1107        1108        1109        1110 
## 0.224586233 0.561736809 0.099887701 0.170255196 0.190440310 0.255781705 
##        1111        1112        1113        1114        1115        1116 
## 0.191098065 0.006504324 0.054229391 0.243286900 0.215960627 0.423517544 
##        1117        1118        1119        1120        1121        1122 
## 0.007209921 0.110344404 0.143493468 0.053374864 0.378928180 0.261147926 
##        1123        1124        1125        1126        1127        1128 
## 0.202662562 0.264852933 0.055110959 0.061975301 0.034219028 0.240280962 
##        1129        1130        1131        1132        1133        1134 
## 0.208103910 0.035918632 0.181590691 0.134156591 0.153258622 0.156818344 
##        1135        1136        1137        1138        1139        1140 
## 0.067959474 0.094488860 0.144174258 0.272280379 0.014307843 0.062554218 
##        1141        1142        1143        1144        1145        1146 
## 0.004334253 0.119583424 0.077008489 0.441256582 0.395548698 0.151302082 
##        1147        1148        1149        1150        1151        1152 
## 0.028497230 0.136539577 0.070076435 0.131886534 0.088834843 0.197978148 
##        1153        1154        1155        1156        1157        1158 
## 0.137765059 0.355515095 0.020938422 0.030096646 0.067233820 0.052291820 
##        1159        1160        1161        1162        1163        1164 
## 0.125599355 0.378017350 0.013256688 0.050074278 0.159398159 0.167127678 
##        1165        1166        1167        1168        1169        1170 
## 0.159024258 0.128684972 0.005672058 0.239967063 0.362116184 0.178913760 
##        1171        1172        1173        1174        1175        1176 
## 0.152045307 0.716301391 0.403011551 0.099116496 0.050816805 0.066830443 
##        1177        1178        1179        1180        1181        1182 
## 0.047485369 0.023644789 0.301219125 0.033329378 0.345351722 0.013174554 
##        1183        1184        1185        1186        1187        1188 
## 0.038256123 0.084208971 0.012060818 0.013554401 0.198365618 0.061447439 
##        1189        1190        1191        1192        1193        1194 
## 0.197187746 0.031335356 0.037894059 0.116489201 0.124617865 0.112033957 
##        1195        1196        1197        1198        1199        1200 
## 0.026575655 0.033322366 0.265374406 0.494323233 0.062511561 0.380315687 
##        1201        1202        1203        1204        1205        1206 
## 0.034342159 0.184811189 0.134440676 0.034368763 0.068679602 0.164760382 
##        1207        1208        1209        1210        1211        1212 
## 0.118326428 0.233333611 0.045123945 0.008049620 0.107146888 0.024394843 
##        1213        1214        1215        1216        1217        1218 
## 0.073930544 0.094388266 0.016537350 0.157623287 0.022959983 0.085633632 
##        1219        1220        1221        1222        1223        1224 
## 0.148059066 0.166448552 0.150667967 0.022905343 0.427704219 0.113424934 
##        1225        1226        1227        1228        1229        1230 
## 0.153481655 0.069683639 0.347806162 0.100435729 0.183361161 0.098975527 
##        1231        1232        1233        1234        1235        1236 
## 0.266965579 0.140843516 0.089368286 0.101880731 0.333875225 0.027010800 
##        1237        1238        1239        1240        1241        1242 
## 0.228250979 0.458997633 0.389441664 0.331901093 0.021049332 0.287061832 
##        1243        1244        1245        1246        1247        1248 
## 0.038298251 0.050868489 0.254534246 0.158846923 0.275416369 0.264367761 
##        1249        1250        1251        1252        1253        1254 
## 0.148627626 0.441692655 0.295599966 0.206247584 0.028860594 0.460946268 
##        1255        1256        1257        1258        1259        1260 
## 0.211765981 0.625581098 0.088001370 0.329080538 0.188730878 0.107197929 
##        1261        1262        1263        1264        1265        1266 
## 0.294337954 0.061324031 0.301287555 0.141955193 0.020352030 0.162080004 
##        1267        1268        1269        1270        1271        1272 
## 0.076350709 0.074916334 0.044568826 0.070943630 0.169043799 0.500394491 
##        1273        1274        1275        1276        1277        1278 
## 0.055872167 0.171877614 0.297331848 0.067750885 0.164962276 0.006312241 
##        1279        1280        1281        1282        1283        1284 
## 0.113583821 0.040631627 0.065699592 0.197665567 0.164255559 0.071410065 
##        1285        1286        1287        1288        1289        1290 
## 0.094748737 0.380179057 0.143617039 0.186608071 0.024606822 0.321786348 
##        1291        1292        1293        1294        1295        1296 
## 0.153886980 0.362983619 0.078629281 0.437190817 0.295990876 0.041540478 
##        1297        1298        1299        1300        1301        1302 
## 0.377039937 0.125026702 0.059605033 0.023784194 0.155455765 0.013701646 
##        1303        1304        1305        1306        1307        1308 
## 0.138846063 0.023200309 0.094987878 0.022930531 0.325214757 0.102578634 
##        1309        1310        1311        1312        1313        1314 
## 0.111286002 0.174086714 0.030856532 0.633893466 0.314234174 0.638948373 
##        1315        1316        1317        1318        1319        1320 
## 0.094293903 0.050848994 0.075680510 0.152123358 0.077641045 0.476031456 
##        1321        1322        1323        1324        1325        1326 
## 0.163013040 0.193321637 0.017353015 0.043259990 0.177965423 0.174787181 
##        1327        1328        1329        1330        1331        1332 
## 0.355586222 0.106638705 0.207525590 0.085467721 0.032435203 0.008654509 
##        1333        1334        1335        1336        1337        1338 
## 0.273567229 0.080395200 0.173096466 0.078684483 0.112279990 0.138633437 
##        1339        1340        1341        1342        1343        1344 
## 0.314863460 0.241080959 0.161650982 0.091136452 0.040144807 0.347248698 
##        1345        1346        1347        1348        1349        1350 
## 0.112299863 0.067096819 0.055914211 0.284727745 0.027833231 0.136767640 
##        1351        1352        1353        1354        1355        1356 
## 0.365590534 0.006229578 0.075101590 0.239471158 0.193717667 0.395123032 
##        1357        1358        1359        1360        1361        1362 
## 0.177956309 0.074016405 0.047855837 0.058812018 0.272354264 0.052236693 
##        1363        1364        1365        1366        1367        1368 
## 0.104231445 0.373494420 0.050479698 0.727608786 0.353820874 0.202187670 
##        1369        1370        1371        1372        1373        1374 
## 0.041513268 0.321081728 0.184758762 0.130181038 0.147221286 0.034133439 
##        1375        1376        1377        1378        1379        1380 
## 0.023731613 0.387245066 0.049746036 0.006813747 0.095096308 0.578783494 
##        1381        1382        1383        1384        1385        1386 
## 0.368687923 0.297129212 0.103442468 0.148379276 0.247122229 0.065200928 
##        1387        1388        1389        1390        1391        1392 
## 0.261776723 0.228961901 0.042685897 0.079328846 0.216708044 0.655550649 
##        1393        1394        1395        1396        1397        1398 
## 0.049899014 0.257432532 0.113645977 0.282949040 0.547526707 0.152813481 
##        1399        1400        1401        1402        1403        1404 
## 0.040043258 0.084143505 0.044678236 0.042875891 0.038041032 0.174757478 
##        1405        1406        1407        1408        1409        1410 
## 0.131325853 0.059862372 0.183266170 0.242272752 0.213103501 0.106116239 
##        1411        1412        1413        1414        1415        1416 
## 0.117272537 0.319979834 0.062391866 0.134124323 0.182035778 0.081817988 
##        1417        1418        1419        1420        1421        1422 
## 0.048995015 0.223861808 0.111510978 0.155629263 0.038581872 0.029373473 
##        1423        1424        1425        1426        1427        1428 
## 0.132124475 0.226531207 0.122261182 0.043941092 0.273049156 0.202117945 
##        1429        1430        1431        1432        1433        1434 
## 0.100702825 0.407607954 0.025873299 0.037643172 0.012580617 0.248870800 
##        1435        1436        1437        1438        1439        1440 
## 0.166561504 0.119085147 0.431724031 0.027450920 0.467087457 0.066346572 
##        1441        1442        1443        1444        1445        1446 
## 0.070999839 0.017353107 0.216544031 0.034447950 0.292718261 0.054007998 
##        1447        1448        1449        1450        1451        1452 
## 0.205727324 0.082048360 0.038900760 0.359649635 0.098794440 0.116046834 
##        1453        1454        1455        1456        1457        1458 
## 0.064523350 0.159210644 0.374344992 0.131853974 0.088732782 0.052976046 
##        1459        1460        1461        1462        1463        1464 
## 0.036010235 0.117660442 0.613047626 0.153189272 0.070188518 0.119545508 
##        1465        1466        1467        1468        1469        1470 
## 0.259058957 0.088686940 0.054833042 0.070940584 0.056512232 0.106520714

attrition_data$Attrition

##    [1] Yes No  Yes No  No  No  No  No  No  No  No  No  No  No  Yes No  No  No 
##   [19] No  No  No  Yes No  No  Yes No  Yes No  No  No  No  No  No  Yes Yes No 
##   [37] Yes No  No  No  No  No  Yes No  No  Yes No  No  No  No  Yes Yes No  No 
##   [55] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No  No 
##   [73] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes
##   [91] No  No  No  No  No  No  No  No  No  No  Yes No  Yes No  No  No  No  Yes
##  [109] No  No  No  Yes No  No  No  No  No  No  No  No  No  No  Yes No  Yes No 
##  [127] Yes Yes No  No  No  No  Yes No  No  No  Yes No  No  No  Yes No  No  No 
##  [145] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No 
##  [163] No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No  Yes No  No 
##  [181] No  No  Yes No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No 
##  [199] No  No  No  No  No  No  Yes Yes No  No  No  No  Yes No  No  No  Yes No 
##  [217] Yes Yes No  No  No  No  No  No  No  No  No  No  No  Yes No  No  No  No 
##  [235] Yes No  Yes No  No  Yes No  No  No  No  No  No  No  No  No  No  Yes No 
##  [253] No  No  No  No  No  No  No  Yes No  No  No  No  Yes No  No  No  No  No 
##  [271] No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No 
##  [289] Yes No  No  No  No  Yes No  No  Yes No  No  No  No  No  No  No  No  No 
##  [307] No  No  No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No  Yes
##  [325] No  No  No  Yes No  No  No  No  No  No  No  No  Yes No  No  No  No  No 
##  [343] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No  No 
##  [361] No  No  No  Yes No  No  Yes No  Yes No  Yes No  No  No  No  No  No  No 
##  [379] Yes No  No  No  Yes No  No  Yes No  No  No  No  No  No  No  No  No  No 
##  [397] No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No 
##  [415] Yes Yes No  No  No  No  No  Yes Yes No  No  No  No  No  No  No  No  No 
##  [433] No  No  No  Yes Yes No  No  Yes Yes No  No  Yes No  No  No  No  No  No 
##  [451] No  No  No  Yes No  No  No  Yes No  No  No  No  No  Yes No  No  No  No 
##  [469] No  Yes No  No  No  No  No  No  No  No  No  Yes Yes No  Yes No  No  No 
##  [487] No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No 
##  [505] Yes No  No  No  No  No  No  No  No  Yes Yes No  No  No  No  No  No  No 
##  [523] No  No  No  Yes No  No  Yes No  No  No  No  No  No  No  No  No  No  No 
##  [541] Yes No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  No  No 
##  [559] No  No  No  No  Yes No  No  No  Yes No  Yes No  No  No  No  Yes No  No 
##  [577] No  No  No  No  No  No  No  No  No  Yes No  No  No  Yes No  Yes No  No 
##  [595] No  Yes No  No  Yes No  No  No  No  No  No  No  No  Yes Yes No  No  No 
##  [613] No  No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  No  No 
##  [631] No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  Yes No  No 
##  [649] No  No  No  No  No  No  No  No  Yes No  No  No  Yes No  Yes Yes No  No 
##  [667] Yes Yes No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  Yes
##  [685] No  No  No  No  Yes Yes No  No  No  Yes No  Yes No  No  No  No  Yes No 
##  [703] No  No  No  No  Yes No  No  Yes No  Yes No  No  No  No  No  No  No  No 
##  [721] Yes No  No  No  No  Yes No  No  No  No  No  Yes Yes No  No  No  No  No 
##  [739] No  No  No  No  No  No  Yes No  No  No  Yes Yes No  No  Yes No  No  No 
##  [757] No  No  No  No  No  Yes Yes No  No  No  No  No  No  No  No  No  No  No 
##  [775] No  No  Yes Yes No  Yes Yes No  No  No  No  No  No  No  No  Yes No  Yes
##  [793] Yes No  No  No  Yes Yes Yes No  Yes Yes No  No  No  No  No  No  No  No 
##  [811] No  No  No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  No 
##  [829] Yes Yes No  Yes No  No  No  No  Yes No  Yes No  No  No  Yes No  No  No 
##  [847] No  No  No  Yes No  No  No  No  No  No  No  Yes No  No  Yes No  No  No 
##  [865] Yes No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  No  No 
##  [883] No  No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No  No  No 
##  [901] No  No  No  No  No  No  No  No  No  No  No  Yes No  Yes No  Yes No  No 
##  [919] No  No  No  No  No  No  No  No  No  No  Yes No  No  No  Yes No  No  No 
##  [937] No  No  No  Yes Yes No  No  No  No  No  Yes Yes No  No  No  No  Yes Yes
##  [955] No  No  No  No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No 
##  [973] No  No  No  Yes No  No  No  No  Yes Yes No  No  No  Yes No  No  No  No 
##  [991] No  No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  Yes Yes
## [1009] No  No  No  No  Yes No  No  No  Yes No  No  No  No  Yes No  No  No  No 
## [1027] No  No  No  No  No  Yes Yes Yes No  No  Yes No  No  Yes No  No  No  No 
## [1045] No  No  No  No  No  No  No  No  No  No  No  No  Yes Yes Yes No  Yes No 
## [1063] No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  Yes No  No 
## [1081] No  No  No  Yes No  Yes No  No  No  No  No  No  No  No  No  No  No  No 
## [1099] No  No  No  No  No  No  No  No  Yes No  No  No  Yes Yes Yes No  No  No 
## [1117] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No 
## [1135] No  No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  No  No 
## [1153] No  Yes No  No  No  No  No  No  No  No  Yes No  No  No  No  Yes No  No 
## [1171] No  Yes No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No 
## [1189] No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No  No  Yes Yes
## [1207] No  No  No  No  No  No  No  Yes No  No  No  No  No  No  No  No  Yes Yes
## [1225] No  No  No  No  No  No  No  No  No  No  No  No  Yes Yes No  No  No  No 
## [1243] No  No  No  No  Yes No  No  Yes No  No  No  No  No  Yes No  Yes No  No 
## [1261] No  No  Yes No  No  No  No  No  No  No  No  Yes No  Yes No  No  No  No 
## [1279] No  Yes No  Yes No  No  No  No  No  No  No  No  Yes Yes No  No  No  No 
## [1297] No  Yes Yes No  No  No  No  No  No  No  No  No  No  No  No  No  Yes Yes
## [1315] No  No  No  No  No  No  No  No  No  No  No  No  Yes No  No  No  No  No 
## [1333] Yes Yes No  No  No  No  Yes Yes No  No  No  No  No  No  No  No  No  No 
## [1351] No  No  No  Yes Yes No  No  No  No  No  No  No  No  No  No  Yes No  No 
## [1369] No  Yes No  No  No  No  No  Yes No  No  No  Yes No  No  No  No  No  No 
## [1387] No  No  No  No  Yes No  No  No  No  Yes Yes No  No  No  No  No  No  No 
## [1405] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No 
## [1423] No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  No  Yes No 
## [1441] No  No  Yes No  Yes No  No  No  No  No  No  No  Yes No  No  No  No  No 
## [1459] No  No  No  Yes No  No  No  No  No  No  No  No 
## Levels: No Yes

pdataN <- as.factor(ifelse(test=as.numeric(pdata>0.5) == 0, yes="No", no="Yes"))

#Each value in the pdata object represents the predicted probability of Attrition being "Yes" for the corresponding observation in your dataset.

# From pROC
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE)

## Setting levels: control = No, case = Yes

## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

par(pty = "s")
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage")

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage")
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691

## If we want to find out the optimal threshold we can store the
## data used to make the ROC graph in a variable...
roc.info <- roc(attrition_data$Attrition, logistic$fitted.values, legacy.axes=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

str(roc.info)

## List of 15
##  $ percent           : logi FALSE
##  $ sensitivities     : num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
##  $ specificities     : num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
##  $ thresholds        : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
##  $ direction         : chr "<"
##  $ cases             : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
##   ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
##  $ controls          : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
##   ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
##  $ fun.sesp          :function (thresholds, controls, cases, direction)  
##  $ auc               : 'auc' num 0.769
##   ..- attr(*, "partial.auc")= logi FALSE
##   ..- attr(*, "percent")= logi FALSE
##   ..- attr(*, "roc")=List of 15
##   .. ..$ percent           : logi FALSE
##   .. ..$ sensitivities     : num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
##   .. ..$ specificities     : num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
##   .. ..$ thresholds        : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
##   .. ..$ direction         : chr "<"
##   .. ..$ cases             : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
##   .. .. ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
##   .. ..$ controls          : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
##   .. .. ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
##   .. ..$ fun.sesp          :function (thresholds, controls, cases, direction)  
##   .. ..$ auc               : 'auc' num 0.769
##   .. .. ..- attr(*, "partial.auc")= logi FALSE
##   .. .. ..- attr(*, "percent")= logi FALSE
##   .. .. ..- attr(*, "roc")=List of 8
##   .. .. .. ..$ percent      : logi FALSE
##   .. .. .. ..$ sensitivities: num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
##   .. .. .. ..$ specificities: num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
##   .. .. .. ..$ thresholds   : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
##   .. .. .. ..$ direction    : chr "<"
##   .. .. .. ..$ cases        : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
##   .. .. .. ..$ controls     : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
##   .. .. .. ..$ fun.sesp     :function (thresholds, controls, cases, direction)  
##   .. .. .. ..- attr(*, "class")= chr "roc"
##   .. ..$ call              : language roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##   .. ..$ original.predictor: Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
##   .. .. ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
##   .. ..$ original.response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
##   .. ..$ predictor         : Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
##   .. .. ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
##   .. ..$ response          : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
##   .. ..$ levels            : chr [1:2] "No" "Yes"
##   .. ..- attr(*, "class")= chr "roc"
##  $ call              : language roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##  $ original.predictor: Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
##   ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
##  $ original.response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
##  $ predictor         : Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
##   ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
##  $ response          : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
##  $ levels            : chr [1:2] "No" "Yes"
##  - attr(*, "class")= chr "roc"

## tpp = true positive percentage
## fpp = false positive precentage
roc.df <- data.frame(tpp=roc.info$sensitivities*100, fpp=(1 - roc.info$specificities)*100,thresholds=roc.info$thresholds)
roc.df

##              tpp        fpp  thresholds
## 1    100.0000000 100.000000        -Inf
## 2    100.0000000  99.918897 0.002818221
## 3    100.0000000  99.837794 0.003621546
## 4    100.0000000  99.756691 0.004351793
## 5    100.0000000  99.675588 0.004477370
## 6    100.0000000  99.594485 0.004686418
## 7    100.0000000  99.513382 0.004926309
## 8    100.0000000  99.432279 0.005121393
## 9    100.0000000  99.351176 0.005219730
## 10   100.0000000  99.270073 0.005285951
## 11   100.0000000  99.188970 0.005491048
## 12   100.0000000  99.107867 0.005733764
## 13   100.0000000  99.026764 0.005919943
## 14   100.0000000  98.945661 0.006119448
## 15   100.0000000  98.864558 0.006212029
## 16   100.0000000  98.783455 0.006270910
## 17   100.0000000  98.702352 0.006321684
## 18   100.0000000  98.621249 0.006412049
## 19   100.0000000  98.540146 0.006498648
## 20    99.5780591  98.540146 0.006548473
## 21    99.5780591  98.459043 0.006610525
## 22    99.5780591  98.377940 0.006659565
## 23    99.5780591  98.296837 0.006752225
## 24    99.5780591  98.215734 0.006819119
## 25    99.5780591  98.134631 0.006856867
## 26    99.5780591  98.053528 0.007049582
## 27    99.5780591  97.972425 0.007219340
## 28    99.5780591  97.891322 0.007501932
## 29    99.5780591  97.810219 0.007826828
## 30    99.5780591  97.729116 0.007964085
## 31    99.5780591  97.648013 0.008170363
## 32    99.1561181  97.648013 0.008309149
## 33    99.1561181  97.566910 0.008387801
## 34    99.1561181  97.485807 0.008454758
## 35    99.1561181  97.404704 0.008557807
## 36    99.1561181  97.323601 0.008784000
## 37    99.1561181  97.242498 0.009030731
## 38    99.1561181  97.161395 0.009249295
## 39    99.1561181  97.080292 0.009384072
## 40    99.1561181  96.999189 0.009510375
## 41    99.1561181  96.918086 0.009655213
## 42    99.1561181  96.836983 0.009768345
## 43    99.1561181  96.755880 0.009857626
## 44    99.1561181  96.674777 0.009937635
## 45    99.1561181  96.593674 0.010066894
## 46    99.1561181  96.512571 0.010146246
## 47    99.1561181  96.431468 0.010229121
## 48    99.1561181  96.350365 0.010547878
## 49    99.1561181  96.269262 0.010830058
## 50    99.1561181  96.188159 0.010880975
## 51    99.1561181  96.107056 0.011161436
## 52    99.1561181  96.025953 0.011482404
## 53    99.1561181  95.944850 0.011681243
## 54    99.1561181  95.863747 0.011946904
## 55    99.1561181  95.782644 0.012072208
## 56    98.7341772  95.782644 0.012200763
## 57    98.3122363  95.782644 0.012449273
## 58    98.3122363  95.701541 0.012594761
## 59    98.3122363  95.620438 0.012730775
## 60    97.8902954  95.620438 0.012866716
## 61    97.8902954  95.539335 0.013027671
## 62    97.8902954  95.458232 0.013215621
## 63    97.8902954  95.377129 0.013298621
## 64    97.8902954  95.296026 0.013355332
## 65    97.8902954  95.214923 0.013459002
## 66    97.8902954  95.133820 0.013551147
## 67    97.8902954  95.052717 0.013571815
## 68    97.8902954  94.971614 0.013645437
## 69    97.8902954  94.890511 0.013775180
## 70    97.8902954  94.809408 0.013872361
## 71    97.8902954  94.728305 0.013914885
## 72    97.8902954  94.647202 0.014120802
## 73    97.8902954  94.566099 0.014583533
## 74    97.8902954  94.484996 0.014863324
## 75    97.8902954  94.403893 0.014946110
## 76    97.8902954  94.322790 0.015100827
## 77    97.8902954  94.241687 0.015181099
## 78    97.8902954  94.160584 0.015340643
## 79    97.8902954  94.079481 0.015566563
## 80    97.8902954  93.998378 0.015924799
## 81    97.8902954  93.917275 0.016345091
## 82    97.8902954  93.836172 0.016507556
## 83    97.8902954  93.755069 0.016660200
## 84    97.8902954  93.673966 0.016838439
## 85    97.8902954  93.592863 0.016900176
## 86    97.8902954  93.511760 0.016994053
## 87    97.8902954  93.430657 0.017217300
## 88    97.8902954  93.349554 0.017353061
## 89    97.8902954  93.268451 0.017732195
## 90    97.8902954  93.187348 0.018136803
## 91    97.8902954  93.106245 0.018172539
## 92    97.8902954  93.025142 0.018425252
## 93    97.8902954  92.944039 0.018991444
## 94    97.8902954  92.862936 0.019702205
## 95    97.8902954  92.781833 0.020092637
## 96    97.4683544  92.781833 0.020104054
## 97    97.4683544  92.700730 0.020160719
## 98    97.4683544  92.619627 0.020280684
## 99    97.4683544  92.538524 0.020466532
## 100   97.4683544  92.457421 0.020618622
## 101   97.4683544  92.376318 0.020797316
## 102   97.4683544  92.295215 0.020952988
## 103   97.4683544  92.214112 0.021006157
## 104   97.4683544  92.133009 0.021047046
## 105   97.4683544  92.051906 0.021105595
## 106   97.4683544  91.970803 0.021187058
## 107   97.4683544  91.889700 0.021294109
## 108   97.4683544  91.808597 0.021492797
## 109   97.4683544  91.727494 0.021796356
## 110   97.4683544  91.646391 0.022155664
## 111   97.4683544  91.565288 0.022616796
## 112   97.4683544  91.484185 0.022917937
## 113   97.4683544  91.403082 0.022945257
## 114   97.4683544  91.321979 0.022991781
## 115   97.4683544  91.240876 0.023068726
## 116   97.4683544  91.159773 0.023157091
## 117   97.4683544  91.078670 0.023230913
## 118   97.4683544  90.997567 0.023369828
## 119   97.4683544  90.916464 0.023561465
## 120   97.4683544  90.835361 0.023688201
## 121   97.4683544  90.754258 0.023757903
## 122   97.4683544  90.673155 0.023807541
## 123   97.4683544  90.592052 0.023862802
## 124   97.4683544  90.510949 0.023897394
## 125   97.4683544  90.429846 0.023975121
## 126   97.0464135  90.429846 0.024125842
## 127   97.0464135  90.348743 0.024252276
## 128   97.0464135  90.267640 0.024317086
## 129   97.0464135  90.186537 0.024362988
## 130   97.0464135  90.105434 0.024465306
## 131   97.0464135  90.024331 0.024571295
## 132   97.0464135  89.943228 0.024751984
## 133   97.0464135  89.862125 0.025054240
## 134   97.0464135  89.781022 0.025240924
## 135   97.0464135  89.699919 0.025325346
## 136   97.0464135  89.618816 0.025500143
## 137   97.0464135  89.537713 0.025746704
## 138   97.0464135  89.456610 0.026030796
## 139   97.0464135  89.375507 0.026234053
## 140   97.0464135  89.294404 0.026339010
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## 517   88.1856540  60.421736 0.081077581
## 518   88.1856540  60.340633 0.081218206
## 519   88.1856540  60.259530 0.081229777
## 520   87.7637131  60.259530 0.081370773
## 521   87.7637131  60.178427 0.081528897
## 522   87.7637131  60.097324 0.081558357
## 523   87.7637131  60.016221 0.081593506
## 524   87.3417722  60.016221 0.081664662
## 525   87.3417722  59.935118 0.081763308
## 526   87.3417722  59.854015 0.081821083
## 527   87.3417722  59.772912 0.081936269
## 528   87.3417722  59.691809 0.082050577
## 529   87.3417722  59.610706 0.082064718
## 530   87.3417722  59.529603 0.082153452
## 531   87.3417722  59.448500 0.082302532
## 532   87.3417722  59.367397 0.082379744
## 533   87.3417722  59.286294 0.082450934
## 534   87.3417722  59.205191 0.082789198
## 535   87.3417722  59.124088 0.083117162
## 536   87.3417722  59.042985 0.083282767
## 537   87.3417722  58.961882 0.083413881
## 538   87.3417722  58.880779 0.083442996
## 539   87.3417722  58.799676 0.083489497
## 540   87.3417722  58.718573 0.083571217
## 541   87.3417722  58.637470 0.083643690
## 542   87.3417722  58.556367 0.083765366
## 543   87.3417722  58.475264 0.083906029
## 544   87.3417722  58.394161 0.083981234
## 545   87.3417722  58.313058 0.084045377
## 546   87.3417722  58.231955 0.084113202
## 547   87.3417722  58.150852 0.084176238
## 548   87.3417722  58.069749 0.084211968
## 549   87.3417722  57.988646 0.084467016
## 550   87.3417722  57.907543 0.084860720
## 551   87.3417722  57.826440 0.085118247
## 552   86.9198312  57.826440 0.085339924
## 553   86.9198312  57.745337 0.085456724
## 554   86.9198312  57.664234 0.085550677
## 555   86.9198312  57.583131 0.085812105
## 556   86.9198312  57.502028 0.086078254
## 557   86.9198312  57.420925 0.086218658
## 558   86.9198312  57.339822 0.086322394
## 559   86.9198312  57.258719 0.086468412
## 560   86.9198312  57.177616 0.086654590
## 561   86.9198312  57.096513 0.086838647
## 562   86.9198312  57.015410 0.087006433
## 563   86.9198312  56.934307 0.087083578
## 564   86.9198312  56.853204 0.087128867
## 565   86.9198312  56.772101 0.087184004
## 566   86.9198312  56.690998 0.087308744
## 567   86.9198312  56.609895 0.087580632
## 568   86.4978903  56.609895 0.087741163
## 569   86.0759494  56.609895 0.087756256
## 570   86.0759494  56.528792 0.087825128
## 571   86.0759494  56.447689 0.087940783
## 572   86.0759494  56.366586 0.088277506
## 573   86.0759494  56.285483 0.088571755
## 574   86.0759494  56.204380 0.088638403
## 575   86.0759494  56.123277 0.088709861
## 576   86.0759494  56.042174 0.088783813
## 577   86.0759494  55.961071 0.088861331
## 578   86.0759494  55.879968 0.089128052
## 579   86.0759494  55.798865 0.089442611
## 580   86.0759494  55.717762 0.089567838
## 581   86.0759494  55.636659 0.089683866
## 582   85.6540084  55.636659 0.089796673
## 583   85.6540084  55.555556 0.090042719
## 584   85.6540084  55.474453 0.090304785
## 585   85.6540084  55.393350 0.090532851
## 586   85.6540084  55.312247 0.090760681
## 587   85.6540084  55.231144 0.090980299
## 588   85.6540084  55.150041 0.091245759
## 589   85.6540084  55.068938 0.091513694
## 590   85.6540084  54.987835 0.092239958
## 591   85.2320675  54.987835 0.092884042
## 592   85.2320675  54.906732 0.093058268
## 593   85.2320675  54.825629 0.093157859
## 594   85.2320675  54.744526 0.093431655
## 595   85.2320675  54.663423 0.093998771
## 596   85.2320675  54.582320 0.094341085
## 597   84.8101266  54.582320 0.094438563
## 598   84.8101266  54.501217 0.094602015
## 599   84.8101266  54.420114 0.094731953
## 600   84.8101266  54.339011 0.094868308
## 601   84.8101266  54.257908 0.095042093
## 602   84.8101266  54.176805 0.095279083
## 603   84.8101266  54.095702 0.095689832
## 604   84.3881857  54.095702 0.096128338
## 605   84.3881857  54.014599 0.096343608
## 606   84.3881857  53.933496 0.096438752
## 607   84.3881857  53.852393 0.096533657
## 608   84.3881857  53.771290 0.096588481
## 609   84.3881857  53.690187 0.096668843
## 610   84.3881857  53.609084 0.096724534
## 611   84.3881857  53.527981 0.096772756
## 612   84.3881857  53.446878 0.096833751
## 613   84.3881857  53.365775 0.096994849
## 614   84.3881857  53.284672 0.097299726
## 615   84.3881857  53.203569 0.097667425
## 616   84.3881857  53.122466 0.097854184
## 617   83.9662447  53.122466 0.097897410
## 618   83.9662447  53.041363 0.098159192
## 619   83.9662447  52.960260 0.098419418
## 620   83.9662447  52.879157 0.098627130
## 621   83.9662447  52.798054 0.098871832
## 622   83.9662447  52.716951 0.098962375
## 623   83.9662447  52.635848 0.099017978
## 624   83.9662447  52.554745 0.099069147
## 625   83.9662447  52.473642 0.099097180
## 626   83.9662447  52.392539 0.099152253
## 627   83.9662447  52.311436 0.099238481
## 628   83.9662447  52.230333 0.099408971
## 629   83.9662447  52.149230 0.099537755
## 630   83.9662447  52.068127 0.099549038
## 631   83.9662447  51.987024 0.099643786
## 632   83.9662447  51.905921 0.099778814
## 633   83.5443038  51.905921 0.099845985
## 634   83.5443038  51.824818 0.099879029
## 635   83.1223629  51.824818 0.099927844
## 636   83.1223629  51.743715 0.100106037
## 637   83.1223629  51.662612 0.100339908
## 638   83.1223629  51.581509 0.100569277
## 639   83.1223629  51.500406 0.100719072
## 640   83.1223629  51.419303 0.100746392
## 641   83.1223629  51.338200 0.100838090
## 642   83.1223629  51.257097 0.100920614
## 643   83.1223629  51.175994 0.101118031
## 644   82.7004219  51.175994 0.101438500
## 645   82.7004219  51.094891 0.101584851
## 646   82.7004219  51.013788 0.101654977
## 647   82.7004219  50.932685 0.101792217
## 648   82.7004219  50.851582 0.101931717
## 649   82.7004219  50.770479 0.101982996
## 650   82.7004219  50.689376 0.101983347
## 651   82.7004219  50.608273 0.102041991
## 652   82.7004219  50.527170 0.102131849
## 653   82.7004219  50.446067 0.102190071
## 654   82.7004219  50.364964 0.102226010
## 655   82.7004219  50.283861 0.102406817
## 656   82.7004219  50.202758 0.102587957
## 657   82.7004219  50.121655 0.102601511
## 658   82.7004219  50.040552 0.102805833
## 659   82.7004219  49.959448 0.103019675
## 660   82.7004219  49.878345 0.103090042
## 661   82.7004219  49.797242 0.103151785
## 662   82.2784810  49.797242 0.103299690
## 663   82.2784810  49.716139 0.103541740
## 664   82.2784810  49.635036 0.103936228
## 665   82.2784810  49.553933 0.104533669
## 666   81.8565401  49.553933 0.104924188
## 667   81.8565401  49.472830 0.105253790
## 668   81.8565401  49.391727 0.105544134
## 669   81.8565401  49.310624 0.105621817
## 670   81.8565401  49.229521 0.105812866
## 671   81.8565401  49.148418 0.106045754
## 672   81.8565401  49.067315 0.106146733
## 673   81.8565401  48.986212 0.106282180
## 674   81.8565401  48.905109 0.106428312
## 675   81.8565401  48.824006 0.106495102
## 676   81.8565401  48.742903 0.106579709
## 677   81.8565401  48.661800 0.106740019
## 678   81.8565401  48.580697 0.106867960
## 679   81.8565401  48.499594 0.106963209
## 680   81.8565401  48.418491 0.107089360
## 681   81.8565401  48.337388 0.107172409
## 682   81.8565401  48.256285 0.107214538
## 683   81.8565401  48.175182 0.107363123
## 684   81.8565401  48.094079 0.107498381
## 685   81.8565401  48.012976 0.107549558
## 686   81.8565401  47.931873 0.107601417
## 687   81.8565401  47.850770 0.107986869
## 688   81.8565401  47.769667 0.108528613
## 689   81.8565401  47.688564 0.108751076
## 690   81.8565401  47.607461 0.109014439
## 691   81.8565401  47.526358 0.109326802
## 692   81.8565401  47.445255 0.109714510
## 693   81.8565401  47.364152 0.110008101
## 694   81.8565401  47.283049 0.110184795
## 695   81.8565401  47.201946 0.110605406
## 696   81.8565401  47.120843 0.110873397
## 697   81.8565401  47.039740 0.110955544
## 698   81.8565401  46.958637 0.111042071
## 699   81.4345992  46.958637 0.111111436
## 700   81.4345992  46.877534 0.111227717
## 701   81.4345992  46.796431 0.111398490
## 702   81.4345992  46.715328 0.111589702
## 703   81.4345992  46.634225 0.111692482
## 704   81.4345992  46.553122 0.111761369
## 705   81.4345992  46.472019 0.111838846
## 706   81.4345992  46.390916 0.111952725
## 707   81.4345992  46.309813 0.112050974
## 708   81.4345992  46.228710 0.112173991
## 709   81.4345992  46.147607 0.112289927
## 710   81.4345992  46.066504 0.112333205
## 711   81.4345992  45.985401 0.112370656
## 712   81.4345992  45.904298 0.112407912
## 713   81.4345992  45.823195 0.112443461
## 714   81.4345992  45.742092 0.112647743
## 715   81.4345992  45.660989 0.112958017
## 716   81.4345992  45.579886 0.113084286
## 717   81.4345992  45.498783 0.113169252
## 718   81.4345992  45.417680 0.113291846
## 719   81.4345992  45.336577 0.113386140
## 720   81.0126582  45.336577 0.113504377
## 721   81.0126582  45.255474 0.113614899
## 722   81.0126582  45.174371 0.113712744
## 723   81.0126582  45.093268 0.113793422
## 724   81.0126582  45.012165 0.113826152
## 725   81.0126582  44.931062 0.113911161
## 726   81.0126582  44.849959 0.114038609
## 727   81.0126582  44.768856 0.114139382
## 728   81.0126582  44.687753 0.114271154
## 729   81.0126582  44.606650 0.114391450
## 730   81.0126582  44.525547 0.114547684
## 731   81.0126582  44.444444 0.114746631
## 732   81.0126582  44.363341 0.114870651
## 733   81.0126582  44.282238 0.114933055
## 734   81.0126582  44.201135 0.114943661
## 735   81.0126582  44.120032 0.115098420
## 736   81.0126582  44.038929 0.115264623
## 737   81.0126582  43.957826 0.115307201
## 738   81.0126582  43.876723 0.115338946
## 739   81.0126582  43.795620 0.115405132
## 740   81.0126582  43.714517 0.115540359
## 741   81.0126582  43.633414 0.115718931
## 742   81.0126582  43.552311 0.115936607
## 743   81.0126582  43.471208 0.116133214
## 744   81.0126582  43.390105 0.116221117
## 745   80.5907173  43.390105 0.116355921
## 746   80.5907173  43.309002 0.116594727
## 747   80.5907173  43.227899 0.116716665
## 748   80.5907173  43.146796 0.116791696
## 749   80.5907173  43.065693 0.117015624
## 750   80.5907173  42.984590 0.117226735
## 751   80.5907173  42.903487 0.117433124
## 752   80.5907173  42.822384 0.117627076
## 753   80.5907173  42.741281 0.117993435
## 754   80.5907173  42.660178 0.118497739
## 755   80.5907173  42.579075 0.118753144
## 756   80.1687764  42.579075 0.118961192
## 757   80.1687764  42.497972 0.119315328
## 758   80.1687764  42.416869 0.119564466
## 759   80.1687764  42.335766 0.119723582
## 760   80.1687764  42.254663 0.119904451
## 761   80.1687764  42.173560 0.119953317
## 762   80.1687764  42.092457 0.120354824
## 763   80.1687764  42.011354 0.120822188
## 764   80.1687764  41.930251 0.120943990
## 765   80.1687764  41.849148 0.121092375
## 766   80.1687764  41.768045 0.121194392
## 767   80.1687764  41.686942 0.121257427
## 768   79.7468354  41.686942 0.121502577
## 769   79.3248945  41.686942 0.121696610
## 770   79.3248945  41.605839 0.121743259
## 771   79.3248945  41.524736 0.122020297
## 772   79.3248945  41.443633 0.122485543
## 773   79.3248945  41.362530 0.123078819
## 774   78.9029536  41.362530 0.123592916
## 775   78.4810127  41.362530 0.123739625
## 776   78.4810127  41.281427 0.123834402
## 777   78.4810127  41.200324 0.124059617
## 778   78.4810127  41.119221 0.124262788
## 779   78.4810127  41.038118 0.124449153
## 780   78.4810127  40.957015 0.124591089
## 781   78.4810127  40.875912 0.124735663
## 782   78.4810127  40.794809 0.124866405
## 783   78.4810127  40.713706 0.124953026
## 784   78.0590717  40.713706 0.125278397
## 785   78.0590717  40.632603 0.125564724
## 786   78.0590717  40.551500 0.125880971
## 787   78.0590717  40.470397 0.126349847
## 788   78.0590717  40.389294 0.126828219
## 789   78.0590717  40.308191 0.127155809
## 790   78.0590717  40.227088 0.127367858
## 791   78.0590717  40.145985 0.128114199
## 792   78.0590717  40.064882 0.128861654
## 793   77.6371308  40.064882 0.129095828
## 794   77.6371308  39.983779 0.129234853
## 795   77.6371308  39.902676 0.129464530
## 796   77.6371308  39.821573 0.129674042
## 797   77.6371308  39.740470 0.129765370
## 798   77.2151899  39.740470 0.129882319
## 799   77.2151899  39.659367 0.130075174
## 800   77.2151899  39.578264 0.130310323
## 801   77.2151899  39.497161 0.130677808
## 802   77.2151899  39.416058 0.131120931
## 803   77.2151899  39.334955 0.131467463
## 804   77.2151899  39.253852 0.131731524
## 805   77.2151899  39.172749 0.131870254
## 806   77.2151899  39.091646 0.131902821
## 807   77.2151899  39.010543 0.132021792
## 808   77.2151899  38.929440 0.132211208
## 809   77.2151899  38.848337 0.132384524
## 810   77.2151899  38.767234 0.132769244
## 811   76.7932489  38.767234 0.133353953
## 812   76.7932489  38.686131 0.133703579
## 813   76.7932489  38.605028 0.133770280
## 814   76.7932489  38.523925 0.133949125
## 815   76.7932489  38.442822 0.134140457
## 816   76.7932489  38.361719 0.134298634
## 817   76.7932489  38.280616 0.134521495
## 818   76.7932489  38.199513 0.134729429
## 819   76.7932489  38.118410 0.134944813
## 820   76.7932489  38.037307 0.135156990
## 821   76.3713080  38.037307 0.135325531
## 822   76.3713080  37.956204 0.135375137
## 823   76.3713080  37.875101 0.135449296
## 824   76.3713080  37.793998 0.135552198
## 825   76.3713080  37.712895 0.135718114
## 826   76.3713080  37.631792 0.136194945
## 827   76.3713080  37.550689 0.136652339
## 828   75.9493671  37.550689 0.136766371
## 829   75.9493671  37.469586 0.137009718
## 830   75.9493671  37.388483 0.137494702
## 831   75.9493671  37.307380 0.137746358
## 832   75.9493671  37.226277 0.137760082
## 833   75.9493671  37.145174 0.137868017
## 834   75.9493671  37.064071 0.138006313
## 835   75.9493671  36.982968 0.138259951
## 836   75.9493671  36.901865 0.138515672
## 837   75.9493671  36.820762 0.138593265
## 838   75.9493671  36.739659 0.138662428
## 839   75.9493671  36.658556 0.138768741
## 840   75.9493671  36.577453 0.138980892
## 841   75.9493671  36.496350 0.139136381
## 842   75.9493671  36.415247 0.139816343
## 843   75.9493671  36.334144 0.140541769
## 844   75.9493671  36.253041 0.140725705
## 845   75.9493671  36.171938 0.140950882
## 846   75.9493671  36.090835 0.141135942
## 847   75.9493671  36.009732 0.141303170
## 848   75.9493671  35.928629 0.141417808
## 849   75.9493671  35.847526 0.141699054
## 850   75.9493671  35.766423 0.142189680
## 851   75.9493671  35.685320 0.142619922
## 852   75.9493671  35.604217 0.142899023
## 853   75.9493671  35.523114 0.143180399
## 854   75.9493671  35.442011 0.143435948
## 855   75.9493671  35.360908 0.143517094
## 856   75.9493671  35.279805 0.143578880
## 857   75.9493671  35.198702 0.143895649
## 858   75.5274262  35.198702 0.144259639
## 859   75.1054852  35.198702 0.144361782
## 860   75.1054852  35.117599 0.144458122
## 861   74.6835443  35.117599 0.144692689
## 862   74.6835443  35.036496 0.144914158
## 863   74.6835443  34.955393 0.145340615
## 864   74.6835443  34.874290 0.146375239
## 865   74.6835443  34.793187 0.147070491
## 866   74.6835443  34.712084 0.147156191
## 867   74.6835443  34.630981 0.147299684
## 868   74.6835443  34.549878 0.147391415
## 869   74.6835443  34.468775 0.147731906
## 870   74.6835443  34.387672 0.148087966
## 871   74.6835443  34.306569 0.148248071
## 872   74.6835443  34.225466 0.148408396
## 873   74.6835443  34.144363 0.148532571
## 874   74.6835443  34.063260 0.148909478
## 875   74.6835443  33.982157 0.149299645
## 876   74.2616034  33.982157 0.149801385
## 877   74.2616034  33.901054 0.150431389
## 878   74.2616034  33.819951 0.150712196
## 879   74.2616034  33.738848 0.150791762
## 880   74.2616034  33.657745 0.151023181
## 881   74.2616034  33.576642 0.151260672
## 882   74.2616034  33.495539 0.151377903
## 883   73.8396624  33.495539 0.151605814
## 884   73.8396624  33.414436 0.151788734
## 885   73.8396624  33.333333 0.151932436
## 886   73.8396624  33.252230 0.152084332
## 887   73.8396624  33.171127 0.152446302
## 888   73.8396624  33.090024 0.152791363
## 889   73.8396624  33.008921 0.152999186
## 890   73.8396624  32.927818 0.153187081
## 891   73.4177215  32.927818 0.153223947
## 892   73.4177215  32.846715 0.153285240
## 893   73.4177215  32.765612 0.153396756
## 894   73.4177215  32.684509 0.153486519
## 895   73.4177215  32.603406 0.153675337
## 896   73.4177215  32.522303 0.153873135
## 897   72.9957806  32.522303 0.153896153
## 898   72.9957806  32.441200 0.153917047
## 899   72.9957806  32.360097 0.154081359
## 900   72.9957806  32.278994 0.154328751
## 901   72.9957806  32.197891 0.154562323
## 902   72.9957806  32.116788 0.154874149
## 903   72.9957806  32.035685 0.155058534
## 904   72.9957806  31.954582 0.155262815
## 905   72.9957806  31.873479 0.155542514
## 906   72.9957806  31.792376 0.155721089
## 907   72.9957806  31.711273 0.155862007
## 908   72.9957806  31.630170 0.156096030
## 909   72.9957806  31.549067 0.156293855
## 910   72.9957806  31.467964 0.156562546
## 911   72.9957806  31.386861 0.156825332
## 912   72.9957806  31.305758 0.156966936
## 913   72.9957806  31.224655 0.157282065
## 914   72.9957806  31.143552 0.157542933
## 915   72.9957806  31.062449 0.157892467
## 916   72.9957806  30.981346 0.158287096
## 917   72.9957806  30.900243 0.158457140
## 918   72.9957806  30.819140 0.158561975
## 919   72.5738397  30.819140 0.158734568
## 920   72.5738397  30.738037 0.158935590
## 921   72.5738397  30.656934 0.159101371
## 922   72.5738397  30.575831 0.159194565
## 923   72.5738397  30.494728 0.159304402
## 924   72.1518987  30.494728 0.160105078
## 925   72.1518987  30.413625 0.161074603
## 926   72.1518987  30.332522 0.161494095
## 927   72.1518987  30.251419 0.161810460
## 928   72.1518987  30.170316 0.162024971
## 929   72.1518987  30.089213 0.162137776
## 930   72.1518987  30.008110 0.162366102
## 931   72.1518987  29.927007 0.162586685
## 932   72.1518987  29.845904 0.162824877
## 933   72.1518987  29.764801 0.163327320
## 934   71.7299578  29.764801 0.163643646
## 935   71.7299578  29.683698 0.163810617
## 936   71.7299578  29.602595 0.164115550
## 937   71.7299578  29.521492 0.164507971
## 938   71.3080169  29.521492 0.164803675
## 939   71.3080169  29.440389 0.164904622
## 940   71.3080169  29.359286 0.165038422
## 941   71.3080169  29.278183 0.165117658
## 942   71.3080169  29.197080 0.165240952
## 943   71.3080169  29.115977 0.165385924
## 944   71.3080169  29.034874 0.165568786
## 945   71.3080169  28.953771 0.165788824
## 946   71.3080169  28.872668 0.166048191
## 947   71.3080169  28.791565 0.166347084
## 948   71.3080169  28.710462 0.166505028
## 949   71.3080169  28.629359 0.166839969
## 950   71.3080169  28.548256 0.167123056
## 951   71.3080169  28.467153 0.167191013
## 952   71.3080169  28.386050 0.167483992
## 953   71.3080169  28.304947 0.168215332
## 954   71.3080169  28.223844 0.168855815
## 955   71.3080169  28.142741 0.169019200
## 956   71.3080169  28.061638 0.169081806
## 957   71.3080169  27.980535 0.169210360
## 958   70.8860759  27.980535 0.169447499
## 959   70.8860759  27.899432 0.169651093
## 960   70.8860759  27.818329 0.169892730
## 961   70.8860759  27.737226 0.170166281
## 962   70.8860759  27.656123 0.170387815
## 963   70.8860759  27.575020 0.170582178
## 964   70.4641350  27.575020 0.170664006
## 965   70.4641350  27.493917 0.170870096
## 966   70.4641350  27.412814 0.171135735
## 967   70.0421941  27.412814 0.171546490
## 968   69.6202532  27.412814 0.171945608
## 969   69.1983122  27.412814 0.172047615
## 970   69.1983122  27.331711 0.172306921
## 971   69.1983122  27.250608 0.172756719
## 972   68.7763713  27.250608 0.173031447
## 973   68.7763713  27.169505 0.173089068
## 974   68.7763713  27.088402 0.173201932
## 975   68.7763713  27.007299 0.173346469
## 976   68.7763713  26.926196 0.173736127
## 977   68.7763713  26.845093 0.174217124
## 978   68.7763713  26.763990 0.174552506
## 979   68.7763713  26.682887 0.174772329
## 980   68.7763713  26.601784 0.174790531
## 981   68.7763713  26.520681 0.174874399
## 982   68.3544304  26.520681 0.175021000
## 983   68.3544304  26.439578 0.175129638
## 984   68.3544304  26.358475 0.175267971
## 985   68.3544304  26.277372 0.175426458
## 986   67.9324895  26.277372 0.175562464
## 987   67.9324895  26.196269 0.175970298
## 988   67.9324895  26.115166 0.176454247
## 989   67.9324895  26.034063 0.176903586
## 990   67.9324895  25.952960 0.177579910
## 991   67.9324895  25.871857 0.177960866
## 992   67.9324895  25.790754 0.178439591
## 993   67.9324895  25.709651 0.178920074
## 994   67.9324895  25.628548 0.179267121
## 995   67.9324895  25.547445 0.180411793
## 996   67.9324895  25.466342 0.181325425
## 997   67.9324895  25.385239 0.181445402
## 998   67.9324895  25.304136 0.181474829
## 999   67.9324895  25.223033 0.181542332
## 1000  67.9324895  25.141930 0.181813234
## 1001  67.9324895  25.060827 0.182650974
## 1002  67.9324895  24.979724 0.183313666
## 1003  67.9324895  24.898621 0.183420768
## 1004  67.5105485  24.898621 0.183834490
## 1005  67.5105485  24.817518 0.184473683
## 1006  67.5105485  24.736415 0.184784975
## 1007  67.0886076  24.736415 0.185145452
## 1008  67.0886076  24.655312 0.185525589
## 1009  67.0886076  24.574209 0.185890980
## 1010  67.0886076  24.493106 0.186359155
## 1011  66.6666667  24.493106 0.186557942
## 1012  66.6666667  24.412003 0.186611517
## 1013  66.6666667  24.330900 0.186916228
## 1014  66.6666667  24.249797 0.187295941
## 1015  66.6666667  24.168694 0.187529915
## 1016  66.6666667  24.087591 0.187973879
## 1017  66.6666667  24.006488 0.188475549
## 1018  66.6666667  23.925385 0.188709830
## 1019  66.6666667  23.844282 0.189044912
## 1020  66.6666667  23.763179 0.189472138
## 1021  66.6666667  23.682076 0.190012821
## 1022  66.6666667  23.600973 0.190455153
## 1023  66.6666667  23.519870 0.190614877
## 1024  66.6666667  23.438767 0.190928912
## 1025  66.2447257  23.438767 0.192046165
## 1026  66.2447257  23.357664 0.193157951
## 1027  66.2447257  23.276561 0.193519652
## 1028  65.8227848  23.276561 0.193788936
## 1029  65.8227848  23.195458 0.193876491
## 1030  65.4008439  23.195458 0.194173391
## 1031  65.4008439  23.114355 0.195224056
## 1032  64.9789030  23.114355 0.196095347
## 1033  64.9789030  23.033252 0.196259655
## 1034  64.9789030  22.952149 0.196520772
## 1035  64.9789030  22.871046 0.196953283
## 1036  64.9789030  22.789943 0.197331082
## 1037  64.5569620  22.789943 0.197507851
## 1038  64.5569620  22.708840 0.197556336
## 1039  64.5569620  22.627737 0.197618478
## 1040  64.1350211  22.627737 0.197821858
## 1041  64.1350211  22.546634 0.198054475
## 1042  64.1350211  22.465531 0.198248210
## 1043  63.7130802  22.465531 0.198727781
## 1044  63.7130802  22.384428 0.199172775
## 1045  63.2911392  22.384428 0.199275636
## 1046  63.2911392  22.303325 0.199324683
## 1047  63.2911392  22.222222 0.199429207
## 1048  63.2911392  22.141119 0.199547414
## 1049  62.8691983  22.141119 0.199863124
## 1050  62.8691983  22.060016 0.200229266
## 1051  62.8691983  21.978913 0.200892577
## 1052  62.8691983  21.897810 0.201625243
## 1053  62.8691983  21.816707 0.201952837
## 1054  62.8691983  21.735604 0.202152808
## 1055  62.8691983  21.654501 0.202425116
## 1056  62.8691983  21.573398 0.202935676
## 1057  62.8691983  21.492295 0.203394852
## 1058  62.8691983  21.411192 0.203812822
## 1059  62.8691983  21.330089 0.204075003
## 1060  62.8691983  21.248986 0.204636777
## 1061  62.8691983  21.167883 0.205447801
## 1062  62.8691983  21.086780 0.205894500
## 1063  62.8691983  21.005677 0.206114212
## 1064  62.8691983  20.924574 0.206207166
## 1065  62.8691983  20.843471 0.206270667
## 1066  62.4472574  20.843471 0.206592781
## 1067  62.4472574  20.762368 0.207158820
## 1068  62.4472574  20.681265 0.207475709
## 1069  62.4472574  20.600162 0.207647152
## 1070  62.4472574  20.519059 0.207936312
## 1071  62.4472574  20.437956 0.208133422
## 1072  62.4472574  20.356853 0.208216489
## 1073  62.0253165  20.356853 0.208721526
## 1074  62.0253165  20.275750 0.209286164
## 1075  62.0253165  20.194647 0.209507403
## 1076  62.0253165  20.113544 0.209748276
## 1077  62.0253165  20.032441 0.209940208
## 1078  61.6033755  20.032441 0.210563842
## 1079  61.6033755  19.951338 0.211285304
## 1080  61.6033755  19.870235 0.211559434
## 1081  61.6033755  19.789132 0.211721288
## 1082  61.6033755  19.708029 0.211852438
## 1083  61.6033755  19.626926 0.211955374
## 1084  61.1814346  19.626926 0.212537677
## 1085  61.1814346  19.545823 0.213195144
## 1086  61.1814346  19.464720 0.213392072
## 1087  61.1814346  19.383617 0.213571054
## 1088  61.1814346  19.302514 0.213733613
## 1089  61.1814346  19.221411 0.214368744
## 1090  61.1814346  19.140308 0.215296755
## 1091  60.7594937  19.140308 0.215744759
## 1092  60.7594937  19.059205 0.215817677
## 1093  60.3375527  19.059205 0.215892480
## 1094  60.3375527  18.978102 0.216027306
## 1095  60.3375527  18.896999 0.216319008
## 1096  59.9156118  18.896999 0.216626037
## 1097  59.4936709  18.896999 0.216752417
## 1098  59.4936709  18.815896 0.217262555
## 1099  59.0717300  18.815896 0.217760231
## 1100  59.0717300  18.734793 0.217947899
## 1101  59.0717300  18.653690 0.218884062
## 1102  59.0717300  18.572587 0.220563332
## 1103  59.0717300  18.491484 0.221704072
## 1104  59.0717300  18.410381 0.222094848
## 1105  59.0717300  18.329278 0.222347869
## 1106  59.0717300  18.248175 0.222575542
## 1107  59.0717300  18.167072 0.222757345
## 1108  59.0717300  18.085969 0.222860425
## 1109  58.6497890  18.085969 0.223195465
## 1110  58.2278481  18.085969 0.223546839
## 1111  57.8059072  18.085969 0.223734905
## 1112  57.8059072  18.004866 0.224224021
## 1113  57.8059072  17.923763 0.224733345
## 1114  57.8059072  17.842660 0.224889708
## 1115  57.8059072  17.761557 0.225713178
## 1116  57.8059072  17.680454 0.226529302
## 1117  57.8059072  17.599351 0.227004281
## 1118  57.8059072  17.518248 0.227720010
## 1119  57.3839662  17.518248 0.228106822
## 1120  56.9620253  17.518248 0.228409525
## 1121  56.9620253  17.437145 0.228605560
## 1122  56.9620253  17.356042 0.228657566
## 1123  56.5400844  17.356042 0.228816992
## 1124  56.5400844  17.274939 0.229168186
## 1125  56.5400844  17.193836 0.229627102
## 1126  56.5400844  17.112733 0.230004033
## 1127  56.5400844  17.031630 0.230240856
## 1128  56.5400844  16.950527 0.231089663
## 1129  56.5400844  16.869424 0.232477860
## 1130  56.5400844  16.788321 0.233183055
## 1131  56.5400844  16.707218 0.233284975
## 1132  56.5400844  16.626115 0.234264282
## 1133  56.5400844  16.545012 0.235434625
## 1134  56.5400844  16.463909 0.235765229
## 1135  56.5400844  16.382806 0.236033874
## 1136  56.5400844  16.301703 0.236296303
## 1137  56.5400844  16.220600 0.236422831
## 1138  56.5400844  16.139497 0.237698035
## 1139  56.1181435  16.139497 0.239025433
## 1140  56.1181435  16.058394 0.239141324
## 1141  56.1181435  15.977291 0.239218123
## 1142  55.6962025  15.977291 0.239372096
## 1143  55.2742616  15.977291 0.239570725
## 1144  54.8523207  15.977291 0.239773869
## 1145  54.8523207  15.896188 0.239892612
## 1146  54.8523207  15.815085 0.239912573
## 1147  54.4303797  15.815085 0.239942215
## 1148  54.0084388  15.815085 0.240124012
## 1149  54.0084388  15.733982 0.240329638
## 1150  54.0084388  15.652879 0.240467576
## 1151  54.0084388  15.571776 0.240596401
## 1152  54.0084388  15.490673 0.240858461
## 1153  53.5864979  15.490673 0.241126465
## 1154  53.5864979  15.409570 0.241690171
## 1155  53.5864979  15.328467 0.242240562
## 1156  53.5864979  15.247364 0.242285172
## 1157  53.5864979  15.166261 0.242370158
## 1158  53.1645570  15.166261 0.242667430
## 1159  53.1645570  15.085158 0.243089518
## 1160  53.1645570  15.004055 0.243503500
## 1161  53.1645570  14.922952 0.243926744
## 1162  53.1645570  14.841849 0.244195145
## 1163  53.1645570  14.760746 0.244545602
## 1164  53.1645570  14.679643 0.244945166
## 1165  53.1645570  14.598540 0.245304206
## 1166  53.1645570  14.517437 0.245692400
## 1167  53.1645570  14.436334 0.245861806
## 1168  52.7426160  14.436334 0.246506710
## 1169  52.7426160  14.355231 0.247683496
## 1170  52.7426160  14.274128 0.248557782
## 1171  52.7426160  14.193025 0.250194992
## 1172  52.7426160  14.111922 0.252155319
## 1173  52.7426160  14.030819 0.253017053
## 1174  52.7426160  13.949716 0.253840377
## 1175  52.7426160  13.868613 0.254486175
## 1176  52.7426160  13.787510 0.254902912
## 1177  52.7426160  13.706407 0.255307422
## 1178  52.7426160  13.625304 0.255562486
## 1179  52.7426160  13.544201 0.255790030
## 1180  52.7426160  13.463098 0.256615444
## 1181  52.7426160  13.381995 0.258077787
## 1182  52.3206751  13.381995 0.258891000
## 1183  52.3206751  13.300892 0.259133891
## 1184  52.3206751  13.219789 0.259225664
## 1185  51.8987342  13.219789 0.259582772
## 1186  51.8987342  13.138686 0.260535483
## 1187  51.8987342  13.057583 0.261462324
## 1188  51.8987342  12.976480 0.262303395
## 1189  51.8987342  12.895377 0.262862423
## 1190  51.8987342  12.814274 0.263473924
## 1191  51.8987342  12.733171 0.264210416
## 1192  51.8987342  12.652068 0.264460467
## 1193  51.4767932  12.652068 0.264703053
## 1194  51.4767932  12.570965 0.265113669
## 1195  51.4767932  12.489862 0.265909926
## 1196  51.4767932  12.408759 0.266466832
## 1197  51.0548523  12.408759 0.266726899
## 1198  51.0548523  12.327656 0.267246044
## 1199  51.0548523  12.246553 0.267888112
## 1200  51.0548523  12.165450 0.268427064
## 1201  51.0548523  12.084347 0.268819123
## 1202  50.6329114  12.084347 0.269152307
## 1203  50.6329114  12.003244 0.269448648
## 1204  50.6329114  11.922141 0.269809381
## 1205  50.6329114  11.841038 0.270036536
## 1206  50.2109705  11.841038 0.270909233
## 1207  50.2109705  11.759935 0.271987893
## 1208  50.2109705  11.678832 0.272259264
## 1209  50.2109705  11.597729 0.272317321
## 1210  50.2109705  11.516626 0.272385107
## 1211  49.7890295  11.516626 0.272732552
## 1212  49.7890295  11.435523 0.273063548
## 1213  49.7890295  11.354420 0.273221201
## 1214  49.3670886  11.354420 0.273465845
## 1215  48.9451477  11.354420 0.273910478
## 1216  48.9451477  11.273317 0.274262406
## 1217  48.9451477  11.192214 0.274843727
## 1218  48.5232068  11.192214 0.276091415
## 1219  48.1012658  11.192214 0.276921178
## 1220  47.6793249  11.192214 0.277651863
## 1221  47.2573840  11.192214 0.278272072
## 1222  47.2573840  11.111111 0.279245086
## 1223  46.8354430  11.111111 0.281418611
## 1224  46.8354430  11.030008 0.282806201
## 1225  46.4135021  11.030008 0.283722655
## 1226  46.4135021  10.948905 0.284612008
## 1227  46.4135021  10.867802 0.284963911
## 1228  46.4135021  10.786699 0.285496732
## 1229  46.4135021  10.705596 0.285834122
## 1230  45.9915612  10.705596 0.285914327
## 1231  45.5696203  10.705596 0.286132077
## 1232  45.5696203  10.624493 0.286686094
## 1233  45.5696203  10.543390 0.288936973
## 1234  45.1476793  10.543390 0.291765188
## 1235  44.7257384  10.543390 0.292772107
## 1236  44.7257384  10.462287 0.293042544
## 1237  44.7257384  10.381184 0.293358538
## 1238  44.7257384  10.300081 0.293521223
## 1239  44.3037975  10.300081 0.293596815
## 1240  44.3037975  10.218978 0.293773123
## 1241  44.3037975  10.137875 0.294137537
## 1242  44.3037975  10.056772 0.294624286
## 1243  43.8818565  10.056772 0.295114296
## 1244  43.8818565   9.975669 0.295458969
## 1245  43.8818565   9.894566 0.295795421
## 1246  43.8818565   9.813463 0.296090410
## 1247  43.8818565   9.732360 0.296248797
## 1248  43.4599156   9.732360 0.296603325
## 1249  43.4599156   9.651257 0.297014106
## 1250  43.4599156   9.570154 0.297230530
## 1251  43.4599156   9.489051 0.297901443
## 1252  43.4599156   9.407948 0.298679471
## 1253  43.0379747   9.407948 0.299012529
## 1254  42.6160338   9.407948 0.299342740
## 1255  42.6160338   9.326845 0.300149194
## 1256  42.1940928   9.326845 0.300754811
## 1257  42.1940928   9.245742 0.300948748
## 1258  42.1940928   9.164639 0.301178532
## 1259  42.1940928   9.083536 0.301253340
## 1260  41.7721519   9.083536 0.302118869
## 1261  41.3502110   9.083536 0.303082913
## 1262  40.9282700   9.083536 0.304234491
## 1263  40.5063291   9.083536 0.306239923
## 1264  40.5063291   9.002433 0.307280272
## 1265  40.5063291   8.921330 0.307435422
## 1266  40.5063291   8.840227 0.307735107
## 1267  40.5063291   8.759124 0.308292783
## 1268  40.5063291   8.678021 0.310680912
## 1269  40.5063291   8.596918 0.313432256
## 1270  40.0843882   8.596918 0.314194511
## 1271  39.6624473   8.596918 0.314421260
## 1272  39.2405063   8.596918 0.314735903
## 1273  38.8185654   8.596918 0.315359608
## 1274  38.8185654   8.515815 0.316328864
## 1275  38.8185654   8.434712 0.318018050
## 1276  38.3966245   8.434712 0.319606981
## 1277  38.3966245   8.353609 0.320530781
## 1278  37.9746835   8.353609 0.321434038
## 1279  37.9746835   8.272506 0.321935967
## 1280  37.5527426   8.272506 0.322108031
## 1281  37.1308017   8.272506 0.322378066
## 1282  37.1308017   8.191403 0.323920206
## 1283  37.1308017   8.110300 0.325440203
## 1284  37.1308017   8.029197 0.325796741
## 1285  36.7088608   8.029197 0.326613563
## 1286  36.7088608   7.948094 0.327647431
## 1287  36.7088608   7.866991 0.328120083
## 1288  36.7088608   7.785888 0.328662567
## 1289  36.2869198   7.785888 0.330063202
## 1290  36.2869198   7.704785 0.331090817
## 1291  35.8649789   7.704785 0.331518430
## 1292  35.8649789   7.623682 0.332420712
## 1293  35.8649789   7.542579 0.333353047
## 1294  35.8649789   7.461476 0.333820494
## 1295  35.8649789   7.380373 0.333903137
## 1296  35.8649789   7.299270 0.334114610
## 1297  35.8649789   7.218167 0.336610624
## 1298  35.8649789   7.137064 0.339422125
## 1299  35.8649789   7.055961 0.340141943
## 1300  35.4430380   7.055961 0.341101209
## 1301  35.4430380   6.974858 0.342982074
## 1302  35.0210970   6.974858 0.344738084
## 1303  35.0210970   6.893755 0.345443053
## 1304  34.5991561   6.893755 0.345925564
## 1305  34.5991561   6.812652 0.346782721
## 1306  34.5991561   6.731549 0.347527430
## 1307  34.5991561   6.650446 0.348442367
## 1308  34.5991561   6.569343 0.349254913
## 1309  34.1772152   6.569343 0.350458354
## 1310  33.7552743   6.569343 0.352156299
## 1311  33.7552743   6.488240 0.353324010
## 1312  33.7552743   6.407137 0.353902847
## 1313  33.7552743   6.326034 0.354749957
## 1314  33.3333333   6.326034 0.355550658
## 1315  32.9113924   6.326034 0.356104085
## 1316  32.9113924   6.244931 0.356854948
## 1317  32.9113924   6.163828 0.357459965
## 1318  32.9113924   6.082725 0.357855172
## 1319  32.9113924   6.001622 0.358446793
## 1320  32.4894515   6.001622 0.359332429
## 1321  32.4894515   5.920519 0.360413573
## 1322  32.4894515   5.839416 0.361601706
## 1323  32.4894515   5.758313 0.362032343
## 1324  32.0675105   5.758313 0.362077485
## 1325  32.0675105   5.677210 0.362348770
## 1326  31.6455696   5.677210 0.362782487
## 1327  31.2236287   5.677210 0.363017855
## 1328  31.2236287   5.596107 0.363583406
## 1329  31.2236287   5.515004 0.364121094
## 1330  30.8016878   5.515004 0.364859001
## 1331  30.8016878   5.433901 0.366273876
## 1332  30.3797468   5.433901 0.367822571
## 1333  30.3797468   5.352798 0.369064001
## 1334  30.3797468   5.271695 0.370845720
## 1335  30.3797468   5.190592 0.372561765
## 1336  29.9578059   5.190592 0.373093176
## 1337  29.5358650   5.190592 0.373404301
## 1338  29.5358650   5.109489 0.373607564
## 1339  29.1139241   5.109489 0.373934016
## 1340  29.1139241   5.028386 0.374246158
## 1341  29.1139241   4.947283 0.374708179
## 1342  29.1139241   4.866180 0.375216775
## 1343  29.1139241   4.785077 0.376201061
## 1344  29.1139241   4.703974 0.377528644
## 1345  29.1139241   4.622871 0.378472765
## 1346  29.1139241   4.541768 0.379553619
## 1347  29.1139241   4.460665 0.380247372
## 1348  29.1139241   4.379562 0.381586046
## 1349  29.1139241   4.298459 0.383465666
## 1350  28.6919831   4.298459 0.384248864
## 1351  28.6919831   4.217356 0.385547313
## 1352  28.6919831   4.136253 0.386958445
## 1353  28.2700422   4.136253 0.387718024
## 1354  28.2700422   4.055150 0.388518891
## 1355  27.8481013   4.055150 0.389144232
## 1356  27.8481013   3.974047 0.390602007
## 1357  27.8481013   3.892944 0.392369866
## 1358  27.8481013   3.811841 0.392988802
## 1359  27.4261603   3.811841 0.393287238
## 1360  27.0042194   3.811841 0.393895314
## 1361  27.0042194   3.730738 0.394315363
## 1362  26.5822785   3.730738 0.394768691
## 1363  26.5822785   3.649635 0.395335865
## 1364  26.5822785   3.568532 0.396036870
## 1365  26.1603376   3.568532 0.398023993
## 1366  26.1603376   3.487429 0.401267247
## 1367  26.1603376   3.406326 0.403726856
## 1368  25.7383966   3.406326 0.406025058
## 1369  25.7383966   3.325223 0.408050274
## 1370  25.3164557   3.325223 0.408727181
## 1371  25.3164557   3.244120 0.409080720
## 1372  24.8945148   3.244120 0.409242814
## 1373  24.8945148   3.163017 0.409570991
## 1374  24.8945148   3.081914 0.411379741
## 1375  24.8945148   3.000811 0.413178621
## 1376  24.4725738   3.000811 0.415445927
## 1377  24.4725738   2.919708 0.417529189
## 1378  24.4725738   2.838605 0.418098871
## 1379  24.0506329   2.838605 0.419105907
## 1380  24.0506329   2.757502 0.420333244
## 1381  24.0506329   2.676399 0.422274824
## 1382  24.0506329   2.595296 0.423538853
## 1383  24.0506329   2.514193 0.425632190
## 1384  23.6286920   2.514193 0.428184576
## 1385  23.2067511   2.514193 0.429192394
## 1386  22.7848101   2.514193 0.430721942
## 1387  22.7848101   2.433090 0.432345263
## 1388  22.7848101   2.351987 0.435078656
## 1389  22.7848101   2.270884 0.437524202
## 1390  22.7848101   2.189781 0.439557084
## 1391  22.7848101   2.108678 0.441474618
## 1392  22.3628692   2.108678 0.441991729
## 1393  21.9409283   2.108678 0.446336686
## 1394  21.9409283   2.027575 0.452320188
## 1395  21.5189873   2.027575 0.456027684
## 1396  21.0970464   2.027575 0.457847834
## 1397  20.6751055   2.027575 0.458447870
## 1398  20.2531646   2.027575 0.459971951
## 1399  20.2531646   1.946472 0.460969723
## 1400  19.8312236   1.946472 0.461397031
## 1401  19.4092827   1.946472 0.462957851
## 1402  19.4092827   1.865369 0.464468715
## 1403  19.4092827   1.784266 0.464988894
## 1404  19.4092827   1.703163 0.466121317
## 1405  18.9873418   1.703163 0.467457348
## 1406  18.5654008   1.703163 0.469570331
## 1407  18.5654008   1.622060 0.472598698
## 1408  18.1434599   1.622060 0.474331514
## 1409  17.7215190   1.622060 0.475405256
## 1410  17.7215190   1.540957 0.476990199
## 1411  17.2995781   1.540957 0.478595683
## 1412  16.8776371   1.540957 0.480587600
## 1413  16.4556962   1.540957 0.484760284
## 1414  16.4556962   1.459854 0.490255077
## 1415  16.0337553   1.459854 0.492975137
## 1416  15.6118143   1.459854 0.493675574
## 1417  15.6118143   1.378751 0.495671765
## 1418  15.6118143   1.297648 0.497380207
## 1419  15.1898734   1.297648 0.499067304
## 1420  14.7679325   1.297648 0.500822412
## 1421  14.3459916   1.297648 0.502239054
## 1422  14.3459916   1.216545 0.503430459
## 1423  14.3459916   1.135442 0.504056510
## 1424  13.9240506   1.135442 0.506928247
## 1425  13.9240506   1.054339 0.512272476
## 1426  13.5021097   1.054339 0.518452857
## 1427  13.5021097   0.973236 0.523398231
## 1428  13.0801688   0.973236 0.525166630
## 1429  13.0801688   0.892133 0.530507392
## 1430  12.6582278   0.892133 0.537648125
## 1431  12.2362869   0.892133 0.541645907
## 1432  12.2362869   0.811030 0.544159879
## 1433  12.2362869   0.729927 0.546055148
## 1434  11.8143460   0.729927 0.548388034
## 1435  11.3924051   0.729927 0.554057950
## 1436  11.3924051   0.648824 0.559561459
## 1437  10.9704641   0.648824 0.560996594
## 1438  10.9704641   0.567721 0.563133283
## 1439  10.5485232   0.567721 0.571656626
## 1440  10.1265823   0.567721 0.582904268
## 1441  10.1265823   0.486618 0.595956975
## 1442  10.1265823   0.405515 0.605903376
## 1443   9.7046414   0.405515 0.609982735
## 1444   9.7046414   0.324412 0.613824439
## 1445   9.2827004   0.324412 0.620059109
## 1446   8.8607595   0.324412 0.625549032
## 1447   8.4388186   0.324412 0.629281798
## 1448   8.4388186   0.243309 0.633437982
## 1449   8.4388186   0.162206 0.634935276
## 1450   8.0168776   0.162206 0.637462729
## 1451   7.5949367   0.162206 0.639272407
## 1452   7.1729958   0.162206 0.641814723
## 1453   6.7510549   0.162206 0.649791827
## 1454   6.7510549   0.081103 0.658624171
## 1455   6.3291139   0.081103 0.662777882
## 1456   6.3291139   0.000000 0.665001809
## 1457   5.9071730   0.000000 0.673153583
## 1458   5.4852321   0.000000 0.685306652
## 1459   5.0632911   0.000000 0.691532633
## 1460   4.6413502   0.000000 0.693086560
## 1461   4.2194093   0.000000 0.697569955
## 1462   3.7974684   0.000000 0.706977440
## 1463   3.3755274   0.000000 0.714337949
## 1464   2.9535865   0.000000 0.716377357
## 1465   2.5316456   0.000000 0.721248817
## 1466   2.1097046   0.000000 0.726826549
## 1467   1.6877637   0.000000 0.730600502
## 1468   1.2658228   0.000000 0.754031504
## 1469   0.8438819   0.000000 0.819082926
## 1470   0.4219409   0.000000 0.868008547
## 1471   0.0000000   0.000000         Inf

head(roc.df) 

##   tpp       fpp  thresholds
## 1 100 100.00000        -Inf
## 2 100  99.91890 0.002818221
## 3 100  99.83779 0.003621546
## 4 100  99.75669 0.004351793
## 5 100  99.67559 0.004477370
## 6 100  99.59448 0.004686418

## head() will show us the values for the upper right-hand corner of the ROC graph, when the threshold is so low
## Thus TPP = 100% and FPP = 100%
tail(roc.df) 

##            tpp fpp thresholds
## 1466 2.1097046   0  0.7268265
## 1467 1.6877637   0  0.7306005
## 1468 1.2658228   0  0.7540315
## 1469 0.8438819   0  0.8190829
## 1470 0.4219409   0  0.8680085
## 1471 0.0000000   0        Inf

## tail() will show us the values for the lower left-hand corner
## of the ROC graph, when the threshold is so high (infinity)
## that every single sample is called "not obese".
## Thus, TPP = 0% and FPP = 0%
## now let's look at the thresholds between TPP 60% and 80%
roc.df[roc.df$tpp > 60 & roc.df$tpp < 80,]

##           tpp      fpp thresholds
## 768  79.74684 41.68694  0.1215026
## 769  79.32489 41.68694  0.1216966
## 770  79.32489 41.60584  0.1217433
## 771  79.32489 41.52474  0.1220203
## 772  79.32489 41.44363  0.1224855
## 773  79.32489 41.36253  0.1230788
## 774  78.90295 41.36253  0.1235929
## 775  78.48101 41.36253  0.1237396
## 776  78.48101 41.28143  0.1238344
## 777  78.48101 41.20032  0.1240596
## 778  78.48101 41.11922  0.1242628
## 779  78.48101 41.03812  0.1244492
## 780  78.48101 40.95702  0.1245911
## 781  78.48101 40.87591  0.1247357
## 782  78.48101 40.79481  0.1248664
## 783  78.48101 40.71371  0.1249530
## 784  78.05907 40.71371  0.1252784
## 785  78.05907 40.63260  0.1255647
## 786  78.05907 40.55150  0.1258810
## 787  78.05907 40.47040  0.1263498
## 788  78.05907 40.38929  0.1268282
## 789  78.05907 40.30819  0.1271558
## 790  78.05907 40.22709  0.1273679
## 791  78.05907 40.14599  0.1281142
## 792  78.05907 40.06488  0.1288617
## 793  77.63713 40.06488  0.1290958
## 794  77.63713 39.98378  0.1292349
## 795  77.63713 39.90268  0.1294645
## 796  77.63713 39.82157  0.1296740
## 797  77.63713 39.74047  0.1297654
## 798  77.21519 39.74047  0.1298823
## 799  77.21519 39.65937  0.1300752
## 800  77.21519 39.57826  0.1303103
## 801  77.21519 39.49716  0.1306778
## 802  77.21519 39.41606  0.1311209
## 803  77.21519 39.33496  0.1314675
## 804  77.21519 39.25385  0.1317315
## 805  77.21519 39.17275  0.1318703
## 806  77.21519 39.09165  0.1319028
## 807  77.21519 39.01054  0.1320218
## 808  77.21519 38.92944  0.1322112
## 809  77.21519 38.84834  0.1323845
## 810  77.21519 38.76723  0.1327692
## 811  76.79325 38.76723  0.1333540
## 812  76.79325 38.68613  0.1337036
## 813  76.79325 38.60503  0.1337703
## 814  76.79325 38.52393  0.1339491
## 815  76.79325 38.44282  0.1341405
## 816  76.79325 38.36172  0.1342986
## 817  76.79325 38.28062  0.1345215
## 818  76.79325 38.19951  0.1347294
## 819  76.79325 38.11841  0.1349448
## 820  76.79325 38.03731  0.1351570
## 821  76.37131 38.03731  0.1353255
## 822  76.37131 37.95620  0.1353751
## 823  76.37131 37.87510  0.1354493
## 824  76.37131 37.79400  0.1355522
## 825  76.37131 37.71290  0.1357181
## 826  76.37131 37.63179  0.1361949
## 827  76.37131 37.55069  0.1366523
## 828  75.94937 37.55069  0.1367664
## 829  75.94937 37.46959  0.1370097
## 830  75.94937 37.38848  0.1374947
## 831  75.94937 37.30738  0.1377464
## 832  75.94937 37.22628  0.1377601
## 833  75.94937 37.14517  0.1378680
## 834  75.94937 37.06407  0.1380063
## 835  75.94937 36.98297  0.1382600
## 836  75.94937 36.90187  0.1385157
## 837  75.94937 36.82076  0.1385933
## 838  75.94937 36.73966  0.1386624
## 839  75.94937 36.65856  0.1387687
## 840  75.94937 36.57745  0.1389809
## 841  75.94937 36.49635  0.1391364
## 842  75.94937 36.41525  0.1398163
## 843  75.94937 36.33414  0.1405418
## 844  75.94937 36.25304  0.1407257
## 845  75.94937 36.17194  0.1409509
## 846  75.94937 36.09084  0.1411359
## 847  75.94937 36.00973  0.1413032
## 848  75.94937 35.92863  0.1414178
## 849  75.94937 35.84753  0.1416991
## 850  75.94937 35.76642  0.1421897
## 851  75.94937 35.68532  0.1426199
## 852  75.94937 35.60422  0.1428990
## 853  75.94937 35.52311  0.1431804
## 854  75.94937 35.44201  0.1434359
## 855  75.94937 35.36091  0.1435171
## 856  75.94937 35.27981  0.1435789
## 857  75.94937 35.19870  0.1438956
## 858  75.52743 35.19870  0.1442596
## 859  75.10549 35.19870  0.1443618
## 860  75.10549 35.11760  0.1444581
## 861  74.68354 35.11760  0.1446927
## 862  74.68354 35.03650  0.1449142
## 863  74.68354 34.95539  0.1453406
## 864  74.68354 34.87429  0.1463752
## 865  74.68354 34.79319  0.1470705
## 866  74.68354 34.71208  0.1471562
## 867  74.68354 34.63098  0.1472997
## 868  74.68354 34.54988  0.1473914
## 869  74.68354 34.46878  0.1477319
## 870  74.68354 34.38767  0.1480880
## 871  74.68354 34.30657  0.1482481
## 872  74.68354 34.22547  0.1484084
## 873  74.68354 34.14436  0.1485326
## 874  74.68354 34.06326  0.1489095
## 875  74.68354 33.98216  0.1492996
## 876  74.26160 33.98216  0.1498014
## 877  74.26160 33.90105  0.1504314
## 878  74.26160 33.81995  0.1507122
## 879  74.26160 33.73885  0.1507918
## 880  74.26160 33.65775  0.1510232
## 881  74.26160 33.57664  0.1512607
## 882  74.26160 33.49554  0.1513779
## 883  73.83966 33.49554  0.1516058
## 884  73.83966 33.41444  0.1517887
## 885  73.83966 33.33333  0.1519324
## 886  73.83966 33.25223  0.1520843
## 887  73.83966 33.17113  0.1524463
## 888  73.83966 33.09002  0.1527914
## 889  73.83966 33.00892  0.1529992
## 890  73.83966 32.92782  0.1531871
## 891  73.41772 32.92782  0.1532239
## 892  73.41772 32.84672  0.1532852
## 893  73.41772 32.76561  0.1533968
## 894  73.41772 32.68451  0.1534865
## 895  73.41772 32.60341  0.1536753
## 896  73.41772 32.52230  0.1538731
## 897  72.99578 32.52230  0.1538962
## 898  72.99578 32.44120  0.1539170
## 899  72.99578 32.36010  0.1540814
## 900  72.99578 32.27899  0.1543288
## 901  72.99578 32.19789  0.1545623
## 902  72.99578 32.11679  0.1548741
## 903  72.99578 32.03569  0.1550585
## 904  72.99578 31.95458  0.1552628
## 905  72.99578 31.87348  0.1555425
## 906  72.99578 31.79238  0.1557211
## 907  72.99578 31.71127  0.1558620
## 908  72.99578 31.63017  0.1560960
## 909  72.99578 31.54907  0.1562939
## 910  72.99578 31.46796  0.1565625
## 911  72.99578 31.38686  0.1568253
## 912  72.99578 31.30576  0.1569669
## 913  72.99578 31.22466  0.1572821
## 914  72.99578 31.14355  0.1575429
## 915  72.99578 31.06245  0.1578925
## 916  72.99578 30.98135  0.1582871
## 917  72.99578 30.90024  0.1584571
## 918  72.99578 30.81914  0.1585620
## 919  72.57384 30.81914  0.1587346
## 920  72.57384 30.73804  0.1589356
## 921  72.57384 30.65693  0.1591014
## 922  72.57384 30.57583  0.1591946
## 923  72.57384 30.49473  0.1593044
## 924  72.15190 30.49473  0.1601051
## 925  72.15190 30.41363  0.1610746
## 926  72.15190 30.33252  0.1614941
## 927  72.15190 30.25142  0.1618105
## 928  72.15190 30.17032  0.1620250
## 929  72.15190 30.08921  0.1621378
## 930  72.15190 30.00811  0.1623661
## 931  72.15190 29.92701  0.1625867
## 932  72.15190 29.84590  0.1628249
## 933  72.15190 29.76480  0.1633273
## 934  71.72996 29.76480  0.1636436
## 935  71.72996 29.68370  0.1638106
## 936  71.72996 29.60260  0.1641155
## 937  71.72996 29.52149  0.1645080
## 938  71.30802 29.52149  0.1648037
## 939  71.30802 29.44039  0.1649046
## 940  71.30802 29.35929  0.1650384
## 941  71.30802 29.27818  0.1651177
## 942  71.30802 29.19708  0.1652410
## 943  71.30802 29.11598  0.1653859
## 944  71.30802 29.03487  0.1655688
## 945  71.30802 28.95377  0.1657888
## 946  71.30802 28.87267  0.1660482
## 947  71.30802 28.79157  0.1663471
## 948  71.30802 28.71046  0.1665050
## 949  71.30802 28.62936  0.1668400
## 950  71.30802 28.54826  0.1671231
## 951  71.30802 28.46715  0.1671910
## 952  71.30802 28.38605  0.1674840
## 953  71.30802 28.30495  0.1682153
## 954  71.30802 28.22384  0.1688558
## 955  71.30802 28.14274  0.1690192
## 956  71.30802 28.06164  0.1690818
## 957  71.30802 27.98054  0.1692104
## 958  70.88608 27.98054  0.1694475
## 959  70.88608 27.89943  0.1696511
## 960  70.88608 27.81833  0.1698927
## 961  70.88608 27.73723  0.1701663
## 962  70.88608 27.65612  0.1703878
## 963  70.88608 27.57502  0.1705822
## 964  70.46414 27.57502  0.1706640
## 965  70.46414 27.49392  0.1708701
## 966  70.46414 27.41281  0.1711357
## 967  70.04219 27.41281  0.1715465
## 968  69.62025 27.41281  0.1719456
## 969  69.19831 27.41281  0.1720476
## 970  69.19831 27.33171  0.1723069
## 971  69.19831 27.25061  0.1727567
## 972  68.77637 27.25061  0.1730314
## 973  68.77637 27.16951  0.1730891
## 974  68.77637 27.08840  0.1732019
## 975  68.77637 27.00730  0.1733465
## 976  68.77637 26.92620  0.1737361
## 977  68.77637 26.84509  0.1742171
## 978  68.77637 26.76399  0.1745525
## 979  68.77637 26.68289  0.1747723
## 980  68.77637 26.60178  0.1747905
## 981  68.77637 26.52068  0.1748744
## 982  68.35443 26.52068  0.1750210
## 983  68.35443 26.43958  0.1751296
## 984  68.35443 26.35848  0.1752680
## 985  68.35443 26.27737  0.1754265
## 986  67.93249 26.27737  0.1755625
## 987  67.93249 26.19627  0.1759703
## 988  67.93249 26.11517  0.1764542
## 989  67.93249 26.03406  0.1769036
## 990  67.93249 25.95296  0.1775799
## 991  67.93249 25.87186  0.1779609
## 992  67.93249 25.79075  0.1784396
## 993  67.93249 25.70965  0.1789201
## 994  67.93249 25.62855  0.1792671
## 995  67.93249 25.54745  0.1804118
## 996  67.93249 25.46634  0.1813254
## 997  67.93249 25.38524  0.1814454
## 998  67.93249 25.30414  0.1814748
## 999  67.93249 25.22303  0.1815423
## 1000 67.93249 25.14193  0.1818132
## 1001 67.93249 25.06083  0.1826510
## 1002 67.93249 24.97972  0.1833137
## 1003 67.93249 24.89862  0.1834208
## 1004 67.51055 24.89862  0.1838345
## 1005 67.51055 24.81752  0.1844737
## 1006 67.51055 24.73642  0.1847850
## 1007 67.08861 24.73642  0.1851455
## 1008 67.08861 24.65531  0.1855256
## 1009 67.08861 24.57421  0.1858910
## 1010 67.08861 24.49311  0.1863592
## 1011 66.66667 24.49311  0.1865579
## 1012 66.66667 24.41200  0.1866115
## 1013 66.66667 24.33090  0.1869162
## 1014 66.66667 24.24980  0.1872959
## 1015 66.66667 24.16869  0.1875299
## 1016 66.66667 24.08759  0.1879739
## 1017 66.66667 24.00649  0.1884755
## 1018 66.66667 23.92539  0.1887098
## 1019 66.66667 23.84428  0.1890449
## 1020 66.66667 23.76318  0.1894721
## 1021 66.66667 23.68208  0.1900128
## 1022 66.66667 23.60097  0.1904552
## 1023 66.66667 23.51987  0.1906149
## 1024 66.66667 23.43877  0.1909289
## 1025 66.24473 23.43877  0.1920462
## 1026 66.24473 23.35766  0.1931580
## 1027 66.24473 23.27656  0.1935197
## 1028 65.82278 23.27656  0.1937889
## 1029 65.82278 23.19546  0.1938765
## 1030 65.40084 23.19546  0.1941734
## 1031 65.40084 23.11436  0.1952241
## 1032 64.97890 23.11436  0.1960953
## 1033 64.97890 23.03325  0.1962597
## 1034 64.97890 22.95215  0.1965208
## 1035 64.97890 22.87105  0.1969533
## 1036 64.97890 22.78994  0.1973311
## 1037 64.55696 22.78994  0.1975079
## 1038 64.55696 22.70884  0.1975563
## 1039 64.55696 22.62774  0.1976185
## 1040 64.13502 22.62774  0.1978219
## 1041 64.13502 22.54663  0.1980545
## 1042 64.13502 22.46553  0.1982482
## 1043 63.71308 22.46553  0.1987278
## 1044 63.71308 22.38443  0.1991728
## 1045 63.29114 22.38443  0.1992756
## 1046 63.29114 22.30333  0.1993247
## 1047 63.29114 22.22222  0.1994292
## 1048 63.29114 22.14112  0.1995474
## 1049 62.86920 22.14112  0.1998631
## 1050 62.86920 22.06002  0.2002293
## 1051 62.86920 21.97891  0.2008926
## 1052 62.86920 21.89781  0.2016252
## 1053 62.86920 21.81671  0.2019528
## 1054 62.86920 21.73560  0.2021528
## 1055 62.86920 21.65450  0.2024251
## 1056 62.86920 21.57340  0.2029357
## 1057 62.86920 21.49230  0.2033949
## 1058 62.86920 21.41119  0.2038128
## 1059 62.86920 21.33009  0.2040750
## 1060 62.86920 21.24899  0.2046368
## 1061 62.86920 21.16788  0.2054478
## 1062 62.86920 21.08678  0.2058945
## 1063 62.86920 21.00568  0.2061142
## 1064 62.86920 20.92457  0.2062072
## 1065 62.86920 20.84347  0.2062707
## 1066 62.44726 20.84347  0.2065928
## 1067 62.44726 20.76237  0.2071588
## 1068 62.44726 20.68127  0.2074757
## 1069 62.44726 20.60016  0.2076472
## 1070 62.44726 20.51906  0.2079363
## 1071 62.44726 20.43796  0.2081334
## 1072 62.44726 20.35685  0.2082165
## 1073 62.02532 20.35685  0.2087215
## 1074 62.02532 20.27575  0.2092862
## 1075 62.02532 20.19465  0.2095074
## 1076 62.02532 20.11354  0.2097483
## 1077 62.02532 20.03244  0.2099402
## 1078 61.60338 20.03244  0.2105638
## 1079 61.60338 19.95134  0.2112853
## 1080 61.60338 19.87024  0.2115594
## 1081 61.60338 19.78913  0.2117213
## 1082 61.60338 19.70803  0.2118524
## 1083 61.60338 19.62693  0.2119554
## 1084 61.18143 19.62693  0.2125377
## 1085 61.18143 19.54582  0.2131951
## 1086 61.18143 19.46472  0.2133921
## 1087 61.18143 19.38362  0.2135711
## 1088 61.18143 19.30251  0.2137336
## 1089 61.18143 19.22141  0.2143687
## 1090 61.18143 19.14031  0.2152968
## 1091 60.75949 19.14031  0.2157448
## 1092 60.75949 19.05921  0.2158177
## 1093 60.33755 19.05921  0.2158925
## 1094 60.33755 18.97810  0.2160273
## 1095 60.33755 18.89700  0.2163190

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 76.91%

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 76.91%

roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE, partial.auc=c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x=45)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE, partial.auc = c(100, 90), auc.polygon = TRUE,     auc.polygon.col = "#377eb822", print.auc.x = 45)
## 
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Partial area under the curve (specificity 100%-90%): 2.881%

# Lets do two roc plots to understand which model is better
roc(attrition_data$Attrition, logistic_simple$fitted.values, plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, print.auc=TRUE)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic_simple$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic_simple$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 64.27%

# Lets add the other graph
plot.roc(attrition_data$Attrition, logistic$fitted.values, percent=TRUE, col="#4daf4a", lwd=4, print.auc=TRUE, add=TRUE, print.auc.y=40)

## Setting levels: control = No, case = Yes
## Setting direction: controls < cases

legend("bottomright", legend=c("Simple", "Non Simple"), col=c("#377eb8", "#4daf4a"), lwd=4) 

Inference: Not Attrited - Since we are aiming to see how many have not Attrition, based on their background factors. * The accuracy of the model is very less showcasing that it is not a well performing model. However, such low accuracy is a clear indication of model underfitting. * At 95% Confidence interval, model is not significant.

SUMMARY FOR REGRESSION

• We can infer that due to the vary dataset, it was difficult to fit the model well which led to an under-performing model.
• Another aspect that calls to attention the bias present in the data is how majority of our logged data points had a ‘No’ for Attrition with just few “yes” for the data points.

attr <- read.csv("/Users/meet/Desktop/Attrition Data copy.csv")
features <- c("Education", "DistanceFromHome", "EnvironmentSatisfaction", "JobSatisfaction", "Age", "MonthlyIncome", "NumCompaniesWorked", "WorkLifeBalance", "YearsAtCompany")
head(attr)

##   Sr.no             Department MaritalStatus EducationField Attrition Education
## 1     1                  Sales        Single  Life Sciences       Yes         2
## 2     2 Research & Development       Married  Life Sciences        No         1
## 3     3 Research & Development        Single          Other       Yes         2
## 4     4 Research & Development       Married  Life Sciences        No         4
## 5     5 Research & Development       Married        Medical        No         1
## 6     6 Research & Development        Single  Life Sciences        No         2
##   DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age MonthlyIncome
## 1                1                       2               4  41          5993
## 2                8                       3               2  49          5130
## 3                2                       4               3  37          2090
## 4                3                       4               3  33          2909
## 5                2                       1               2  27          3468
## 6                2                       4               4  32          3068
##   NumCompaniesWorked WorkLifeBalance YearsAtCompany
## 1                  8               1              6
## 2                  1               3             10
## 3                  6               3              0
## 4                  1               3              8
## 5                  9               3              2
## 6                  0               2              7

dim(attr)

## [1] 1470   14

str(attr)

## 'data.frame':    1470 obs. of  14 variables:
##  $ Sr.no                  : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Department             : chr  "Sales" "Research & Development" "Research & Development" "Research & Development" ...
##  $ MaritalStatus          : chr  "Single" "Married" "Single" "Married" ...
##  $ EducationField         : chr  "Life Sciences" "Life Sciences" "Other" "Life Sciences" ...
##  $ Attrition              : chr  "Yes" "No" "Yes" "No" ...
##  $ Education              : int  2 1 2 4 1 2 3 1 3 3 ...
##  $ DistanceFromHome       : int  1 8 2 3 2 2 3 24 23 27 ...
##  $ EnvironmentSatisfaction: int  2 3 4 4 1 4 3 4 4 3 ...
##  $ JobSatisfaction        : int  4 2 3 3 2 4 1 3 3 3 ...
##  $ Age                    : int  41 49 37 33 27 32 59 30 38 36 ...
##  $ MonthlyIncome          : int  5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
##  $ NumCompaniesWorked     : int  8 1 6 1 9 0 4 1 0 6 ...
##  $ WorkLifeBalance        : int  1 3 3 3 3 2 2 3 3 2 ...
##  $ YearsAtCompany         : int  6 10 0 8 2 7 1 1 9 7 ...

attr.data <- as.matrix(attr[,c(6:14)])
row.names(attr.data) <- attr$Sr.no
attr_raw <- cbind(attr.data, as.numeric(as.factor(attr$Attrition)) - 1)
# Map numeric values to categorical labels
#test_raw.df$Attrition <- ifelse(test_raw.df$Attrition == 0, "No", "Yes")
colnames(attr_raw)[9] <- "Attrition"
smp_size_raw <- floor(0.75 * nrow(attr_raw))
train_ind_raw <- sample(nrow(attr_raw), size = smp_size_raw)
train_raw.df <- as.data.frame(attr_raw[train_ind_raw, ])
test_raw.df <- as.data.frame(attr_raw[-train_ind_raw, ])
attr_raw.lda <- lda(formula = train_raw.df$Attrition ~ ., data = train_raw.df)
attr_raw.lda

## Call:
## lda(train_raw.df$Attrition ~ ., data = train_raw.df)
## 
## Prior probabilities of groups:
##           0           1           2           3           4           5 
## 0.034482759 0.117967332 0.083484574 0.097096189 0.072595281 0.127949183 
##           6           7           8           9          10          11 
## 0.055353902 0.058983666 0.048094374 0.055353902 0.084392015 0.020871143 
##          12          13          14          15          16          17 
## 0.009981851 0.012704174 0.012704174 0.015426497 0.007259528 0.005444646 
##          18          19          20          21          22          23 
## 0.005444646 0.009074410 0.019963702 0.008166969 0.009981851 0.001814882 
##          24          25          26          27          29          31 
## 0.003629764 0.003629764 0.003629764 0.001814882 0.001814882 0.002722323 
##          32          33          36          37          40 
## 0.002722323 0.002722323 0.000907441 0.000907441 0.000907441 
## 
## Group means:
##    Education DistanceFromHome EnvironmentSatisfaction JobSatisfaction      Age
## 0   2.842105         8.842105                2.710526        2.394737 32.52632
## 1   2.823077         9.776923                2.692308        2.746154 35.25385
## 2   2.750000         9.260870                2.695652        2.750000 34.59783
## 3   2.953271         7.738318                2.654206        2.551402 35.14019
## 4   2.612500         9.137500                2.662500        2.587500 36.96250
## 5   2.858156         8.900709                2.687943        2.702128 36.01418
## 6   2.836066         9.573770                2.737705        3.000000 34.86885
## 7   3.061538         8.230769                3.000000        2.753846 36.12308
## 8   3.018868        10.056604                2.679245        2.698113 37.13208
## 9   2.934426         9.672131                2.803279        2.868852 39.40984
## 10  3.021505        11.268817                2.559140        2.903226 37.17204
## 11  2.826087         7.652174                2.913043        2.782609 34.69565
## 12  2.636364        12.181818                2.727273        3.181818 42.63636
## 13  3.071429         7.428571                2.642857        2.785714 38.21429
## 14  3.500000         6.500000                2.785714        3.214286 39.85714
## 15  3.411765         9.411765                2.529412        2.647059 38.17647
## 16  3.375000         6.375000                2.625000        2.375000 40.12500
## 17  3.000000        12.666667                3.000000        2.833333 41.66667
## 18  3.333333         7.333333                2.333333        2.500000 40.83333
## 19  3.100000         8.300000                2.600000        2.500000 44.50000
## 20  2.727273        13.000000                2.818182        2.772727 43.04545
## 21  2.444444        12.111111                2.888889        2.444444 40.66667
## 22  2.818182         6.454545                2.909091        3.000000 43.45455
## 23  2.000000         5.000000                3.000000        3.000000 46.00000
## 24  3.000000         6.000000                1.750000        1.500000 47.75000
## 25  2.750000        11.000000                2.000000        2.750000 45.75000
## 26  2.750000         3.250000                2.750000        2.000000 47.00000
## 27  3.000000        18.000000                2.000000        3.000000 50.00000
## 29  3.000000         8.000000                2.500000        1.500000 55.50000
## 31  4.000000         7.333333                3.000000        2.000000 52.33333
## 32  3.000000         9.000000                1.666667        3.333333 50.66667
## 33  4.333333         1.666667                2.333333        3.333333 52.33333
## 36  3.000000         1.000000                4.000000        1.000000 55.00000
## 37  4.000000        10.000000                4.000000        3.000000 58.00000
## 40  4.000000        23.000000                4.000000        4.000000 58.00000
##    MonthlyIncome NumCompaniesWorked WorkLifeBalance        V10
## 0       4450.500          3.1842105        2.736842 0.36842105
## 1       4912.938          2.7846154        2.769231 0.33846154
## 2       4922.174          3.5108696        2.695652 0.22826087
## 3       5224.570          2.9158879        2.822430 0.15887850
## 4       5409.050          3.0250000        2.650000 0.16250000
## 5       5500.050          2.6808511        2.751773 0.08510638
## 6       5453.557          2.3934426        2.672131 0.09836066
## 7       6608.954          2.9692308        2.707692 0.13846154
## 8       6878.226          2.8490566        2.867925 0.09433962
## 9       7182.328          1.6557377        2.754098 0.11475410
## 10      6824.817          1.7311828        2.688172 0.13978495
## 11      6126.913          2.0869565        2.826087 0.04347826
## 12      9306.818          3.3636364        2.727273 0.00000000
## 13      7445.286          3.2857143        2.571429 0.14285714
## 14     10309.571          2.2142857        2.714286 0.14285714
## 15      7274.647          1.7647059        2.941176 0.05882353
## 16      9287.125          3.0000000        2.750000 0.12500000
## 17     10512.167          2.6666667        3.166667 0.16666667
## 18     10297.667          3.1666667        2.833333 0.16666667
## 19     11989.700          2.8000000        2.900000 0.10000000
## 20     11038.091          2.3636364        2.772727 0.04545455
## 21     17007.333          1.1111111        2.666667 0.11111111
## 22     17151.545          2.9090909        2.727273 0.09090909
## 23     11842.000          5.0000000        1.500000 0.50000000
## 24     13302.250          3.0000000        3.000000 0.25000000
## 25     16478.000          1.2500000        3.000000 0.00000000
## 26     14692.500          3.5000000        2.000000 0.00000000
## 27     17893.000          2.5000000        2.500000 0.00000000
## 29     19706.500          4.5000000        1.500000 0.00000000
## 31     18890.667          3.0000000        3.000000 0.33333333
## 32     17485.333          1.0000000        3.000000 0.33333333
## 33     16412.000          0.3333333        3.333333 0.33333333
## 36     19045.000          0.0000000        3.000000 0.00000000
## 37     13872.000          0.0000000        2.000000 0.00000000
## 40     10312.000          1.0000000        2.000000 1.00000000
## 
## Coefficients of linear discriminants:
##                                   LD1           LD2           LD3           LD4
## Education                0.0194664362 -3.303152e-01 -9.372866e-02  6.458836e-01
## DistanceFromHome         0.0076650599 -2.944635e-02 -7.391267e-03 -7.226622e-02
## EnvironmentSatisfaction -0.0155544511  4.744783e-02 -8.609406e-02  1.871747e-02
## JobSatisfaction          0.0029752310 -3.084476e-01 -1.470254e-01 -2.040139e-01
## Age                      0.0293813926 -3.814864e-02 -4.016911e-02 -4.090181e-02
## MonthlyIncome            0.0002248072  9.192477e-05  2.145038e-05  3.312454e-05
## NumCompaniesWorked      -0.2065904930  2.979431e-01  4.222096e-02 -1.301104e-02
## WorkLifeBalance          0.0209949570 -3.451268e-01 -1.770520e-01  5.789019e-01
## V10                      0.1722172408  4.552581e-01 -2.784967e+00  1.052412e-01
##                                   LD5           LD6           LD7           LD8
## Education                0.1521563258  2.727383e-01 -1.445411e-01  2.574035e-02
## DistanceFromHome         0.0112006396 -5.000829e-02  5.317659e-03 -3.306848e-02
## EnvironmentSatisfaction  0.3582526472  4.207622e-01  4.121939e-01 -6.001451e-01
## JobSatisfaction          0.5396455021  1.311839e-01 -5.265080e-01  7.304698e-02
## Age                     -0.0907217560  4.596495e-02 -2.713211e-02 -3.151100e-02
## MonthlyIncome            0.0001036935 -5.908247e-05  1.784344e-05  2.449303e-05
## NumCompaniesWorked       0.0506937902 -1.808884e-02 -2.157988e-01 -1.121515e-01
## WorkLifeBalance         -0.1335413466 -8.710694e-01 -2.342870e-01 -7.216141e-01
## V10                      0.2069858973 -1.275450e-01  2.834566e-01  2.136920e-01
##                                   LD9
## Education               -6.005750e-01
## DistanceFromHome        -7.203445e-02
## EnvironmentSatisfaction  7.666822e-02
## JobSatisfaction          2.871335e-01
## Age                      2.661540e-02
## MonthlyIncome           -1.908564e-05
## NumCompaniesWorked      -8.334661e-02
## WorkLifeBalance          4.558913e-01
## V10                      2.105454e-01
## 
## Proportion of trace:
##    LD1    LD2    LD3    LD4    LD5    LD6    LD7    LD8    LD9 
## 0.6192 0.0976 0.0835 0.0650 0.0405 0.0383 0.0221 0.0187 0.0151

summary(attr_raw.lda)

##         Length Class  Mode     
## prior    35    -none- numeric  
## counts   35    -none- numeric  
## means   315    -none- numeric  
## scaling  81    -none- numeric  
## lev      35    -none- character
## svd       9    -none- numeric  
## N         1    -none- numeric  
## call      3    -none- call     
## terms     3    terms  call     
## xlevels   0    -none- list

print(attr_raw.lda)

## Call:
## lda(train_raw.df$Attrition ~ ., data = train_raw.df)
## 
## Prior probabilities of groups:
##           0           1           2           3           4           5 
## 0.034482759 0.117967332 0.083484574 0.097096189 0.072595281 0.127949183 
##           6           7           8           9          10          11 
## 0.055353902 0.058983666 0.048094374 0.055353902 0.084392015 0.020871143 
##          12          13          14          15          16          17 
## 0.009981851 0.012704174 0.012704174 0.015426497 0.007259528 0.005444646 
##          18          19          20          21          22          23 
## 0.005444646 0.009074410 0.019963702 0.008166969 0.009981851 0.001814882 
##          24          25          26          27          29          31 
## 0.003629764 0.003629764 0.003629764 0.001814882 0.001814882 0.002722323 
##          32          33          36          37          40 
## 0.002722323 0.002722323 0.000907441 0.000907441 0.000907441 
## 
## Group means:
##    Education DistanceFromHome EnvironmentSatisfaction JobSatisfaction      Age
## 0   2.842105         8.842105                2.710526        2.394737 32.52632
## 1   2.823077         9.776923                2.692308        2.746154 35.25385
## 2   2.750000         9.260870                2.695652        2.750000 34.59783
## 3   2.953271         7.738318                2.654206        2.551402 35.14019
## 4   2.612500         9.137500                2.662500        2.587500 36.96250
## 5   2.858156         8.900709                2.687943        2.702128 36.01418
## 6   2.836066         9.573770                2.737705        3.000000 34.86885
## 7   3.061538         8.230769                3.000000        2.753846 36.12308
## 8   3.018868        10.056604                2.679245        2.698113 37.13208
## 9   2.934426         9.672131                2.803279        2.868852 39.40984
## 10  3.021505        11.268817                2.559140        2.903226 37.17204
## 11  2.826087         7.652174                2.913043        2.782609 34.69565
## 12  2.636364        12.181818                2.727273        3.181818 42.63636
## 13  3.071429         7.428571                2.642857        2.785714 38.21429
## 14  3.500000         6.500000                2.785714        3.214286 39.85714
## 15  3.411765         9.411765                2.529412        2.647059 38.17647
## 16  3.375000         6.375000                2.625000        2.375000 40.12500
## 17  3.000000        12.666667                3.000000        2.833333 41.66667
## 18  3.333333         7.333333                2.333333        2.500000 40.83333
## 19  3.100000         8.300000                2.600000        2.500000 44.50000
## 20  2.727273        13.000000                2.818182        2.772727 43.04545
## 21  2.444444        12.111111                2.888889        2.444444 40.66667
## 22  2.818182         6.454545                2.909091        3.000000 43.45455
## 23  2.000000         5.000000                3.000000        3.000000 46.00000
## 24  3.000000         6.000000                1.750000        1.500000 47.75000
## 25  2.750000        11.000000                2.000000        2.750000 45.75000
## 26  2.750000         3.250000                2.750000        2.000000 47.00000
## 27  3.000000        18.000000                2.000000        3.000000 50.00000
## 29  3.000000         8.000000                2.500000        1.500000 55.50000
## 31  4.000000         7.333333                3.000000        2.000000 52.33333
## 32  3.000000         9.000000                1.666667        3.333333 50.66667
## 33  4.333333         1.666667                2.333333        3.333333 52.33333
## 36  3.000000         1.000000                4.000000        1.000000 55.00000
## 37  4.000000        10.000000                4.000000        3.000000 58.00000
## 40  4.000000        23.000000                4.000000        4.000000 58.00000
##    MonthlyIncome NumCompaniesWorked WorkLifeBalance        V10
## 0       4450.500          3.1842105        2.736842 0.36842105
## 1       4912.938          2.7846154        2.769231 0.33846154
## 2       4922.174          3.5108696        2.695652 0.22826087
## 3       5224.570          2.9158879        2.822430 0.15887850
## 4       5409.050          3.0250000        2.650000 0.16250000
## 5       5500.050          2.6808511        2.751773 0.08510638
## 6       5453.557          2.3934426        2.672131 0.09836066
## 7       6608.954          2.9692308        2.707692 0.13846154
## 8       6878.226          2.8490566        2.867925 0.09433962
## 9       7182.328          1.6557377        2.754098 0.11475410
## 10      6824.817          1.7311828        2.688172 0.13978495
## 11      6126.913          2.0869565        2.826087 0.04347826
## 12      9306.818          3.3636364        2.727273 0.00000000
## 13      7445.286          3.2857143        2.571429 0.14285714
## 14     10309.571          2.2142857        2.714286 0.14285714
## 15      7274.647          1.7647059        2.941176 0.05882353
## 16      9287.125          3.0000000        2.750000 0.12500000
## 17     10512.167          2.6666667        3.166667 0.16666667
## 18     10297.667          3.1666667        2.833333 0.16666667
## 19     11989.700          2.8000000        2.900000 0.10000000
## 20     11038.091          2.3636364        2.772727 0.04545455
## 21     17007.333          1.1111111        2.666667 0.11111111
## 22     17151.545          2.9090909        2.727273 0.09090909
## 23     11842.000          5.0000000        1.500000 0.50000000
## 24     13302.250          3.0000000        3.000000 0.25000000
## 25     16478.000          1.2500000        3.000000 0.00000000
## 26     14692.500          3.5000000        2.000000 0.00000000
## 27     17893.000          2.5000000        2.500000 0.00000000
## 29     19706.500          4.5000000        1.500000 0.00000000
## 31     18890.667          3.0000000        3.000000 0.33333333
## 32     17485.333          1.0000000        3.000000 0.33333333
## 33     16412.000          0.3333333        3.333333 0.33333333
## 36     19045.000          0.0000000        3.000000 0.00000000
## 37     13872.000          0.0000000        2.000000 0.00000000
## 40     10312.000          1.0000000        2.000000 1.00000000
## 
## Coefficients of linear discriminants:
##                                   LD1           LD2           LD3           LD4
## Education                0.0194664362 -3.303152e-01 -9.372866e-02  6.458836e-01
## DistanceFromHome         0.0076650599 -2.944635e-02 -7.391267e-03 -7.226622e-02
## EnvironmentSatisfaction -0.0155544511  4.744783e-02 -8.609406e-02  1.871747e-02
## JobSatisfaction          0.0029752310 -3.084476e-01 -1.470254e-01 -2.040139e-01
## Age                      0.0293813926 -3.814864e-02 -4.016911e-02 -4.090181e-02
## MonthlyIncome            0.0002248072  9.192477e-05  2.145038e-05  3.312454e-05
## NumCompaniesWorked      -0.2065904930  2.979431e-01  4.222096e-02 -1.301104e-02
## WorkLifeBalance          0.0209949570 -3.451268e-01 -1.770520e-01  5.789019e-01
## V10                      0.1722172408  4.552581e-01 -2.784967e+00  1.052412e-01
##                                   LD5           LD6           LD7           LD8
## Education                0.1521563258  2.727383e-01 -1.445411e-01  2.574035e-02
## DistanceFromHome         0.0112006396 -5.000829e-02  5.317659e-03 -3.306848e-02
## EnvironmentSatisfaction  0.3582526472  4.207622e-01  4.121939e-01 -6.001451e-01
## JobSatisfaction          0.5396455021  1.311839e-01 -5.265080e-01  7.304698e-02
## Age                     -0.0907217560  4.596495e-02 -2.713211e-02 -3.151100e-02
## MonthlyIncome            0.0001036935 -5.908247e-05  1.784344e-05  2.449303e-05
## NumCompaniesWorked       0.0506937902 -1.808884e-02 -2.157988e-01 -1.121515e-01
## WorkLifeBalance         -0.1335413466 -8.710694e-01 -2.342870e-01 -7.216141e-01
## V10                      0.2069858973 -1.275450e-01  2.834566e-01  2.136920e-01
##                                   LD9
## Education               -6.005750e-01
## DistanceFromHome        -7.203445e-02
## EnvironmentSatisfaction  7.666822e-02
## JobSatisfaction          2.871335e-01
## Age                      2.661540e-02
## MonthlyIncome           -1.908564e-05
## NumCompaniesWorked      -8.334661e-02
## WorkLifeBalance          4.558913e-01
## V10                      2.105454e-01
## 
## Proportion of trace:
##    LD1    LD2    LD3    LD4    LD5    LD6    LD7    LD8    LD9 
## 0.6192 0.0976 0.0835 0.0650 0.0405 0.0383 0.0221 0.0187 0.0151

plot(attr_raw.lda)

attr_raw.lda.predict <- predict(attr_raw.lda, newdata = test_raw.df)
attr_raw.lda.predict$class

##   [1] 5  2  10 1  5  10 10 10 5  1  5  5  5  4  20 5  5  5  5  5  5  20 5  5  5 
##  [26] 1  22 1  5  5  5  10 10 5  3  2  10 3  5  5  5  1  5  5  5  5  2  10 1  2 
##  [51] 5  1  5  2  5  2  5  3  22 1  5  25 1  5  5  5  5  1  5  22 10 5  5  5  10
##  [76] 5  5  5  5  10 5  10 10 5  5  5  5  5  7  1  1  5  2  22 5  1  2  5  5  10
## [101] 5  22 5  10 5  10 1  1  20 5  10 5  1  5  1  19 2  9  5  4  10 1  5  5  5 
## [126] 5  3  5  5  10 5  1  5  5  3  5  10 1  5  2  5  10 5  31 10 1  5  5  3  5 
## [151] 5  22 5  10 5  2  1  5  5  5  1  5  5  5  2  5  5  5  5  5  5  5  9  2  23
## [176] 1  10 5  2  3  5  3  5  21 5  5  25 2  5  10 5  9  5  1  2  23 5  0  5  5 
## [201] 10 24 1  5  5  21 5  22 5  10 2  21 10 7  1  5  5  2  3  2  5  5  5  31 5 
## [226] 5  5  5  1  1  1  5  3  5  5  5  5  5  20 5  10 5  1  10 10 22 10 5  9  5 
## [251] 5  9  3  20 1  2  20 1  21 10 1  1  3  3  1  19 5  1  10 1  5  5  5  5  1 
## [276] 5  5  10 5  3  5  5  5  5  3  1  5  5  5  5  1  3  27 5  5  5  5  5  10 5 
## [301] 5  21 5  5  14 5  5  1  1  22 5  5  1  5  9  2  5  3  5  2  5  5  5  5  5 
## [326] 10 3  1  5  3  20 1  5  22 1  1  3  10 1  3  5  5  5  1  3  5  1  5  5  5 
## [351] 5  10 5  5  5  5  2  2  5  10 1  23 2  1  20 5  5  5 
## 35 Levels: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ... 40

attr_raw.lda.predict$x

##              LD1          LD2          LD3          LD4           LD5
## 4    -0.65994100 -1.046642637  0.208931611  1.322116351  0.5321769957
## 5    -2.38566231  2.803676303  1.493589535 -0.235567624 -0.5420505442
## 9     1.31494066 -1.185674452  0.053705581 -0.741404607  0.7858707433
## 15   -1.50199360  0.374639622 -2.200597756 -0.631552018  1.0289973231
## 20   -1.13087679  0.100842717  0.153265568  0.322215725  0.7649546796
## 23    1.69275294 -0.499279106  0.697160745  1.453958669 -0.2367840393
## 28    0.74233166 -1.214178053  0.085351502  0.920692161 -0.7708438262
## 29    0.98023242 -0.764332076  0.090629361  0.540044154 -0.0936780662
## 31   -1.38115968 -0.186912101  0.366924055  0.473054002  0.6594688426
## 34   -0.88979887 -0.682196127 -2.995393125  0.713135093  0.4872293001
## 44    0.49033317 -0.099940908  0.631495426  0.752997946  1.5835394609
## 45   -0.53608092 -0.467267958  0.494385746  0.111358845  0.7732914189
## 59   -0.44347372 -0.179239431  0.438653089  0.405489513  1.8447001393
## 64    0.09620365  0.685945991  0.179783751 -2.125551103 -2.9584129334
## 66    2.46200927 -0.315853376 -0.321672840 -0.205522758 -0.2807041467
## 68    1.05445874  0.154513555  0.445710147  0.479671757 -1.7022691884
## 75   -0.91836480 -0.714711139  0.272350867  0.073530757  0.0793615693
## 86    0.36736989 -0.381058302 -0.400774214 -1.231397858 -0.3853385473
## 93   -0.27071210  0.516541000  0.969012322 -0.236630708 -0.0146315138
## 96    0.69330162  2.091216969  0.551157484 -0.430154911 -0.6830066673
## 104  -0.13376734 -1.140816750  0.445626593  1.071200088 -0.4026831439
## 113   3.15177839 -0.879756084 -0.506401586 -1.584230545  0.8179742912
## 114  -0.66044653 -0.559303019  0.867841905 -1.360307254  0.2790157098
## 117   1.12908624  0.855789670  0.857164674  1.156010076 -0.1707350101
## 122   0.41462794 -1.030002433  0.339236250 -0.458275521 -0.3058009489
## 123  -0.89047229  0.993197406 -2.880188575 -0.177784023 -1.8618444984
## 124   2.41766785  1.682498330  0.425727353  0.139777731 -0.2657487958
## 128  -1.11023351  0.605853256 -1.722333824 -1.930503777  1.7711942264
## 129  -0.91085611 -0.295937134  0.827936875 -0.315854795  1.1531200711
## 134   0.35205684  0.496237025  0.408211104 -1.246188265 -0.2922256090
## 136  -1.13574502  1.301261574  0.827613309 -0.140322130 -0.8026756704
## 139   0.40538621 -0.464968364  0.862645248 -0.682568172  0.9559102788
## 140   0.23445626 -0.426107127  0.703518055 -0.888301216  1.4736697672
## 144  -0.68917893 -0.866256496  0.741690997 -0.929285017 -0.1497441614
## 152   0.40154184 -0.730180600  0.376848100  2.361309484  0.0373900475
## 154  -1.86694692  1.587048542  0.733113958 -1.349071358 -1.3338201877
## 155   0.73247183 -0.669023883  0.461647092  0.316049907  0.9812755189
## 160  -1.80804199  0.324597862  0.458809273  1.247249642  0.2551667145
## 173  -1.43903810  0.971475496  0.709011140 -0.533472690 -0.3834560679
## 174  -0.67531369 -0.194128379  0.762461292  0.760050508 -0.7012518365
## 177  -0.53290352 -1.723443738  0.021074023  1.104132603  0.3235671093
## 183  -0.10223029 -0.156617619 -2.334361975 -1.824821087 -1.1991691870
## 186  -0.63246252 -0.745854066  0.365099841  0.080250165 -0.0522829017
## 194  -1.13507649 -1.050722628 -0.343599707  0.286842521 -0.0092374717
## 196  -0.27249857 -0.471619022  0.666281972 -0.974778953 -1.3755905553
## 198   0.04213953 -0.792314135  0.080676266 -1.592246245 -0.4502769323
## 199  -1.35422549  1.510579360  0.431410199  1.206491025  0.8507769908
## 200  -0.03185075 -0.386851491  0.273063945 -2.684004491  1.4733248873
## 205  -0.56813465  2.098876179 -1.887564028 -2.176516655 -0.9810294807
## 209  -1.63835726  1.125490634  0.376710740 -0.152660186  1.5327284867
## 214   1.22090923  1.095759464  0.496648770 -0.501350142 -0.8376169879
## 217  -0.38597952  1.300261374 -1.818213978 -0.228253191  0.5604029902
## 220   0.40645157 -0.323986499 -0.139603094  0.312712041 -2.2394384394
## 221  -1.34796757  1.765805798  0.591077606  0.554489070 -0.0286310119
## 229   0.72244115 -0.585789031  0.272274877  1.493918336  0.2940996320
## 231  -1.30271768  0.393038061 -0.077215639 -0.898298259 -0.7043772630
## 239  -0.68484849  0.275580148  0.726429492  0.205123403 -0.4114428682
## 241  -1.87516577  0.461336050  0.307597415  1.102028901 -0.1588452216
## 245   3.54574355 -0.271326739  0.081752203  0.659921289  1.0891354874
## 251   0.28260050  1.383834802 -2.072200877  0.227271651  0.2215028858
## 257  -0.29303902 -0.740314913  0.193581126  0.790954212 -1.6104277126
## 258   3.46777377  0.455347714  0.693168053  0.320610619  0.1699020626
## 260  -0.01782307 -0.949734786 -2.474339632 -0.865437388 -0.1155176122
## 270  -0.29103538 -1.497833786 -0.022810664  0.155696251  0.6616207743
## 278   0.12548651  0.027840179  0.776141551 -0.022045614 -2.0554331627
## 279  -0.14569038  0.881492846  1.260668933  0.250108829  0.7235391355
## 286  -0.75273370 -1.191465199 -0.007290639  0.426843136  0.4520452342
## 287  -0.42154810  0.010227386 -2.635432187 -2.361515170  0.2188817158
## 290  -0.71433261 -0.614086524  0.421854318 -0.317203922  1.3187029155
## 301   2.51079342  0.190828256  0.323124085  1.705312278  0.6145637434
## 305   1.19278369 -0.578774674  0.294131168  0.008798970  0.7726904525
## 307  -0.12024493 -0.214131036  0.545551025 -0.065536580  0.9160970789
## 310  -0.04842207 -1.507316483  0.212348094  1.113001296  1.0649828130
## 313  -0.59134733 -0.924155832  0.543022378  0.101573313  1.0780112185
## 316  -0.18941397 -2.329825912 -0.357389122  0.182475810 -0.2130138694
## 319  -0.94567333  0.020178810  0.929818734  0.369228985  0.1377037865
## 326   0.64506486  0.079725936  0.662687714  0.004243871  0.7215443125
## 329  -0.62726061 -0.221799437  0.575609533 -0.617273891  0.7003428471
## 336   0.32038772  0.063640517  0.471979685 -0.794142523  0.0493841298
## 338  -0.22989219 -2.003600594  0.237511221  1.505147800  0.9982374136
## 340  -0.02678249 -0.447619177  0.803096948  1.482251686  0.2190669322
## 342   1.69870098 -0.793305197  0.188190570 -0.966170749  0.9312300488
## 343   0.26132499 -0.709689895  0.466646290  0.453471062  1.5123955229
## 347  -0.75521583  0.975388737  0.384253358  0.374626260 -0.2744932280
## 350  -0.43442844 -0.029210568  0.685103617  0.390840964  1.0456750814
## 351  -0.28731183 -0.734559334  0.175291062 -0.924146507 -1.1830215772
## 352  -0.82504577 -0.437280073  0.571778366  0.956843091 -0.4942471564
## 357   0.10373767 -0.859506244  0.133555452  0.868336094 -0.3277430970
## 359  -0.34277848 -0.502963019  0.069425841  1.870798219  1.4697220899
## 364  -0.50489890 -0.325293600 -2.498333454  0.635020294  0.6033936237
## 367   1.22832154  0.162946463 -2.267474199  0.743375572 -1.0735620203
## 368   0.54936688  0.307722476 -0.205130022 -0.542714799  0.4959922892
## 373  -1.37905753  1.678705651  0.733019270  1.008198730  0.3021005711
## 380   2.86235676 -0.320137939 -0.297436526  0.068379181  0.0308135907
## 381  -0.54600859 -1.130365758  0.370642173  1.808022271  1.4336258413
## 383  -0.49221054  0.955847464 -1.671601873  0.184733850 -0.5504783893
## 386  -2.36214329  1.794218772 -2.105739456  0.484423720  1.3926109106
## 395  -0.42975219  0.913171901  1.297471189 -0.917848130 -0.9297433793
## 397  -0.56940474 -0.580704583  0.017640600  0.547446439 -0.3579510371
## 399  -0.39018663 -1.534817294  0.081582261  0.202090611  0.1124306350
## 400  -0.93425904  0.302553043  0.770738302  0.641823975 -0.7640366318
## 401   3.13538701  1.176678859  0.785457350 -0.214315297  0.4814305454
## 405  -0.35815889  0.113513569  0.909273291 -0.332936193 -0.4282710010
## 410  -0.02481941 -1.187955227  0.178525927 -2.231296267 -1.1506957977
## 413   0.03285411 -0.883583817  0.015737049 -1.487144804 -0.6082487427
## 419  -0.72929789 -0.800865569  0.900886063 -1.901511116  0.9686710569
## 422  -1.29154440 -0.342647973 -2.454530733  1.347121550  0.6343152395
## 423  -0.95258614 -0.194858751 -1.892014984  1.087789522  0.9893261447
## 428   1.37025093 -0.688058850 -0.479121097 -1.061895213 -2.4455813433
## 429  -0.58611440  0.048983959  0.167907562 -0.710638354 -1.1616965174
## 431   0.02855233 -1.528615766  0.068002970 -0.721860535  0.4976746255
## 435   1.04224460  0.471201001  0.748180158  0.053221018  0.0953998250
## 436   0.76408073  2.377528233 -1.905542307 -0.559621462  0.9808417739
## 439  -0.07900580  0.152562873  0.354208598 -0.227617677  0.9860112167
## 441  -0.36920540  2.664642095 -1.715262510 -0.205017818  0.0601575191
## 446   2.88206461 -0.615788408 -0.090918948  0.567298635 -1.2125159782
## 447  -0.90015023  0.887167524  0.200834253 -0.974802471  0.7686691107
## 453   0.31634894 -1.304997724 -0.203555369  1.116408285 -1.2471188156
## 465  -0.11183764 -0.243470765  0.229825594  1.107354540  0.3115361896
## 466   0.69048160  1.101514243  0.624677175 -2.666007094 -0.8841696107
## 468   0.87924589 -0.665156870  0.536308656  1.069036202 -0.7635256804
## 470  -1.49771473  1.462075992 -2.260881988  0.858610241  1.4607871996
## 472   0.67807041  0.070903161  0.368941205  0.150176793  0.4649918136
## 477  -1.03477006 -0.218360790  0.784684378 -0.435151170  0.5804352876
## 479  -1.02840023 -0.214601803  0.892306738 -1.075347435  0.1126803569
## 484  -0.86806148 -0.596124922  0.407922170 -1.914938698 -0.0101447889
## 494  -0.21268193 -0.718265371  0.055728388  1.602336379 -1.2254203288
## 495  -0.62434232 -1.156168865  0.260202659 -0.189246085  0.0200344487
## 502  -0.93768794 -0.725259186  0.491543639  0.752859820  0.2082824645
## 509   0.29600572 -1.271099397  0.211742355  0.905851613  0.5949781987
## 513  -0.77423373 -1.645908055  0.500448925  1.291752300  0.4011101232
## 515  -0.36778693  0.253837485 -1.920557077  1.147891063 -1.5215209346
## 518  -0.23594238 -0.369347593  0.733517883  0.923468927  0.7728313899
## 519  -0.02124878 -1.858698173 -0.186722398  0.674605900  0.7283555060
## 534   0.42963794  1.131594773  0.538193556  1.497875212 -0.1724448824
## 538   0.47431352  1.139662701  1.182981552 -0.206072855  0.5149822207
## 544  -0.17555202 -1.525288208  0.023225467 -1.333974774 -1.3239182651
## 548  -1.17123581  0.352930503 -2.668107735 -0.831643236 -0.1706167247
## 549   0.17180562 -0.805684387 -0.166760282 -0.700995930  0.6521300274
## 552  -1.40292456  2.709477416  1.061284083 -0.530500465 -0.0287216406
## 556  -0.88383485 -0.517667588  0.545495615  0.517718124  0.2182062503
## 559   0.06081980 -1.857038942  0.256621771 -0.335239942  0.5718641297
## 560  -1.54290357  0.655319445  0.490132123  0.617800493  0.7554221830
## 562   3.06429086 -0.265071442 -0.052020113  1.975182283 -1.3164082006
## 564  -0.04421590 -0.137856502  0.827756126 -2.643726075  1.7132123983
## 567   0.26410935 -0.051980014 -2.754666137 -2.132353974 -0.7691800090
## 572  -0.95632162  0.218766634  0.919264194  0.223202015  0.5576645325
## 575  -0.73499261 -1.097194680  0.258886787  1.183576280  0.3313582449
## 580  -0.29770444 -0.350584223  0.587873616  1.791550465 -0.8546522276
## 582  -0.98834084  0.137835935  0.542212197  0.948055602  0.8269850280
## 583  -0.18817231 -0.239886963  0.384352177  0.045820398 -1.1778559220
## 585   3.12567261  0.161650974  0.439327974 -0.359439435  1.1856363444
## 587  -0.93360395 -0.308431735  0.848342276  0.788926361  0.3435280610
## 591   1.56864981 -0.717347262  0.328293524  1.251263087  0.7929717120
## 597  -1.12028664 -0.505206663  0.219173349  1.345473903  0.3879313066
## 598  -1.39070297  1.694478879  0.308024807 -0.396895289  0.6611086719
## 599  -1.34954770  1.551604873 -1.861951398  1.090250674  1.3630692011
## 600  -1.29400726 -0.040821988  0.451591643 -0.048244984 -0.6053841981
## 602  -0.84971079 -0.148257871  0.347917436  0.047512299 -0.5519856878
## 604  -0.44613948 -1.297932661 -0.013410623  0.199208221 -1.5021917054
## 608   1.13046751 -1.371857574 -3.320343960  0.062261734 -0.2350592736
## 616  -1.14415862 -0.561341870  0.547896687  0.098878909  1.4727947811
## 622   0.12709476 -0.197165554  0.563493480 -0.659128670  0.2313383348
## 629  -0.29257637 -0.373367982  0.152299133  0.293466662  0.8221298747
## 631  -1.68987617  2.135568828  1.311241421 -0.740261140  2.4570915881
## 632  -0.49682471 -1.429595750  0.058692821 -0.344228312 -0.7700725335
## 633  -1.34242473  0.382622431  0.321581986 -1.217928655 -0.7669282940
## 634  -0.43310028 -0.853517754  0.643146295  0.538301055 -2.0996783477
## 639  -0.61231211  0.568189086  1.036065740  0.652244830 -0.6187271550
## 643  -0.25403402 -1.169059093  0.334245200  0.217385135 -1.3142657945
## 644  -0.10202828 -0.559041383  0.149287678 -0.429612730  0.1699291513
## 651  -0.44230125  0.135463847  0.129349042 -0.322322482  0.5507688903
## 652   0.29590691 -1.394831900 -0.226818406 -0.625803579 -0.7539288063
## 655  -1.43800977  1.072348659  0.266786817  0.284017714  0.9569680970
## 661  -1.60892001  1.846887472 -2.935238882 -2.365099347 -0.9726673134
## 663  -1.09671212  0.482473489 -1.708125663  0.759191563  1.4407825829
## 665   0.48486093 -0.464757079  0.441079045 -2.199991705  0.5722711757
## 672  -0.77078827 -0.829872719  0.510639036  0.266201140 -0.9818752442
## 673  -0.82438207  0.993520255  0.364519857 -1.119008974 -0.1736965275
## 676  -1.17950887 -0.985583358  0.326841581  1.611087752 -0.0503782214
## 687  -0.22655137 -0.028449494  0.334273489  0.587258076 -1.1528560619
## 693   0.19914095 -0.433388463  0.534048256  2.457633724 -0.5524918717
## 704   0.15947816 -1.215653923  0.048283198 -0.165546894  0.4720921857
## 711   2.69547651  0.207550282  0.510963770  0.145970855  2.0440145649
## 713  -0.89871624 -0.107702337  0.537457096 -1.587681035  0.1685477694
## 714  -0.87655199 -1.216834962 -0.334605429  0.724624497 -0.0041124163
## 717   3.17426927  0.129956124  0.414556686  0.972045604  0.2758245535
## 718  -2.39875941  1.434982895  0.922644799  0.706028230  0.7196060557
## 728  -1.50787235 -0.446814797  0.969450904  0.196349547  1.2415696589
## 730   1.24334588 -0.785575159  0.389558944 -0.699425106  1.1479598981
## 734  -0.33305252 -0.162369816  0.592915852  0.269812289  1.6571279251
## 739   1.65612266  0.369752493  0.327781631 -0.594713196  1.0682398356
## 740  -0.29136941 -1.415881861  0.554644916  1.436296274  0.6161686884
## 745  -0.75253444  1.900926407 -1.640019983 -1.606256554 -0.7892778085
## 748  -1.03664518  0.808159412  0.413567387  0.915989335  0.6663616442
## 759   1.65076649  0.390675748  0.023429430 -2.015885032 -1.0289691285
## 761   0.74425426 -0.466586225 -0.118975229  0.255651076 -1.8141702794
## 763  -1.90767245  1.919986192 -1.448891451  1.398154086 -0.7796240348
## 766  -0.93044361 -0.697036808  0.176734419  1.069952789 -0.1874218789
## 768  -0.72971398  0.490664621  0.576200724  0.151398608 -0.1633581231
## 769   0.92468500 -0.241668350  0.526372481 -1.280040228 -0.7324530134
## 775   1.82434699  2.419340912  0.367230538 -0.094286468 -1.7624496942
## 780  -1.63697291  0.547385980 -2.897082563  1.022680175 -1.7318317285
## 782  -0.64401249  0.510626077  1.267125318  0.847717931 -1.2050701934
## 794  -0.88594640 -0.410372984  0.928815263 -1.290644277 -0.1981286290
## 800   3.07578913  0.975490444  0.610609879  0.644323703 -0.1997156908
## 804  -1.00947441 -0.838365769  0.193774592  1.034779780  0.7314942195
## 805   2.72940877 -0.082960155  0.251497724  0.463990945  0.2472923512
## 807   0.41170370  0.804703586  0.150342843  0.594056369 -1.3172876925
## 808   1.07361729 -1.252887885  0.125297454  0.799186528  0.3526630210
## 812  -0.80355644  1.957127160  0.698568418  0.171193191 -0.0118213347
## 815   3.40522986 -0.163145994  0.207800610  0.708919072  1.1098255650
## 818   0.48103838 -1.307958127  0.235496338  0.003556732  0.4485899895
## 822   1.10806552  0.932554466  0.106429582  0.783549714 -0.0907301831
## 830   1.00042042 -0.102873754 -1.996262259  1.534703655 -0.8472450828
## 834  -0.91587929 -0.609786770  0.513564474  0.692588846  0.9195865319
## 835  -0.00227033  0.237556464  0.815009300 -1.613456169 -0.2399135963
## 838   0.32981769  2.116898285  0.797567546  0.232570044  0.8850290200
## 841  -1.79581031  0.365825368  0.340516536  1.298225890  0.5142966904
## 842  -2.07731502  1.465930854  0.966295624 -0.337515327  1.3182820581
## 844  -0.47628844 -1.091494960  0.633783639  1.398313855  0.7887977186
## 847   0.85437923  0.127663673  0.485983797  1.661844941 -0.0296666012
## 848   0.08246467 -0.152886319  0.581313790  1.281527398 -0.6106971943
## 852   3.22714052  1.123063457  0.063750322  1.242346699 -0.7041174037
## 853  -0.72887936 -0.374377453  0.658544904 -0.902821139  0.3183571246
## 854  -1.13487521  0.508021015  1.286895936  0.546862032  0.0906105371
## 856   0.20620607 -0.445638288  0.263263550 -0.007668919  1.0375865230
## 857  -1.00782105 -0.006213069  1.262852678  0.577009344  0.6310448967
## 858  -0.08924878 -1.262109830 -2.982961290  0.453751011 -0.5358248693
## 861  -0.59838811 -0.830735824 -2.238528819  1.665702145  1.8619944385
## 865  -1.49080026  2.285961543 -1.624374941 -1.233706105 -1.9851820120
## 871   0.46421302  0.186933274  0.619627404  0.792509269 -0.2005421380
## 879  -0.85217884  0.677720908  0.203534473  2.692411272 -0.7033115107
## 882  -0.88606950  0.767443009  0.615422026  0.173681199  0.6760825409
## 889   0.45483786  0.960013716  0.682069317 -1.006077978  1.3438226181
## 890  -0.90318228 -0.053624043  1.177298420 -0.122637299 -1.0428387731
## 892  -0.55504836 -0.979225266  0.147642998 -1.283100348 -1.5616611351
## 898  -0.21480956 -0.664381236 -0.585263280 -0.587062146 -1.3600222871
## 915   2.36164394  0.246902279 -0.054701057 -1.319318855 -1.2976107205
## 927   0.89836573 -0.842190459 -0.282726552  1.432235867  0.9028955767
## 939   0.15383688 -2.780992679 -0.696358093 -1.219693613 -2.6422954620
## 942  -0.10210854 -1.281028038  0.506881337  0.391892162  0.2781270505
## 947   1.06744431 -0.331299113 -2.697910125 -0.052933796  0.5029172221
## 949   1.40922283  0.005520471  0.885403691  1.102040326  0.0993222231
## 950   0.21095598 -1.347508097  0.295423358 -1.288369055 -1.1054064020
## 957   2.79678857  1.271941686 -0.033246027  0.715759657 -0.0417164927
## 959   0.84143231 -0.678466668  0.325878239 -0.382971903  1.5587461371
## 962  -0.27671702 -1.076654906  0.236039693  1.193715925  0.1426307585
## 963   2.37654896 -0.178968173  0.036417129  0.349009720 -0.9757072317
## 964  -0.05202251  0.936805092  0.839073836  0.374645296 -1.5182389123
## 965   0.17606724 -0.257566311  0.539601931  0.196993490 -0.9660564573
## 970   0.89351702 -1.167838344 -0.347277086 -0.048316201  0.0873673146
## 973  -1.40328805 -0.858097937  0.568059415  1.766184674  1.9899557311
## 977   1.88582136 -0.015829448 -0.270287429 -1.197276687 -0.7820752226
## 986   0.31327428 -0.428846938 -2.388936592 -0.334481707  1.6060376301
## 991  -0.08722510  1.278310508  0.686612293 -0.252849195  0.7762602911
## 995   2.14747079 -0.253606780 -0.110578827 -2.802912254  0.0403854504
## 998  -0.67247700 -0.822082738 -2.449545500  0.643982182  1.3869002335
## 1000  2.97744744  0.282549775  0.525269111  0.664674214 -0.4060054618
## 1003  0.73748506 -0.368766467  0.324890599 -1.157437589  1.1156511899
## 1007  0.07171399 -0.080456358 -2.549796337 -1.954094556 -2.6467646768
## 1008  0.68979198  0.001305969 -2.219013751 -1.197504450  1.3810396278
## 1014 -1.54252884  1.526471253  0.887362663  1.547661380  0.2679233933
## 1016 -1.45864394  0.790766647  0.648345894  1.784612501 -0.4484405491
## 1017 -0.83342692 -0.662518434 -2.246019545  1.174120663 -1.0943783920
## 1025  2.60396188 -0.132014135  0.125509862  1.790840655 -0.3773707061
## 1029 -0.76236911 -1.264750553  0.153754431  0.841001732 -0.6323979179
## 1032  0.98730990 -0.175104963 -2.833821286  0.333921665 -0.2964996952
## 1035  1.40746227 -0.124689720  0.373798250 -0.422457769 -1.4397983059
## 1040 -0.40323146 -0.963906142 -2.405852209  0.891174216 -0.3764297808
## 1043 -0.68163231 -0.623159779  0.021980481  0.045421347 -0.8261479802
## 1052 -1.12856729  0.423630012  0.416661483  1.011070427 -0.7802949220
## 1053 -1.10989171 -0.572284868  0.621677208 -0.141904758  0.3027383324
## 1056  1.37590754  2.842908407  1.372820084 -0.051249221  0.5274852616
## 1058 -0.73067948  1.907729298 -1.405985347 -0.744963864  0.2135030172
## 1060 -0.74244494 -0.296201648  0.369381869 -1.003130888 -0.1132981502
## 1062 -1.08656218 -0.109216336  0.812233111 -0.149199989  0.5258855408
## 1064  0.62513650 -0.557339849  0.553673590 -0.145962788  1.1560588264
## 1065 -0.72970395 -1.311183028  0.286645663  1.488675875 -0.0003241278
## 1067 -1.84587535  1.261015142  0.922322055  1.337407040 -0.6198380211
## 1068 -0.22424801 -0.526135477  0.042656337 -1.259247042 -0.7157881421
## 1071 -0.13231810 -0.189026900  0.854529470  1.059883026 -0.4035590729
## 1072 -0.41630149  0.639704934  0.300817697 -0.211528432 -2.3142022640
## 1080  0.15725942  0.576375766  0.602617453  0.522660943 -0.6678850398
## 1081  1.36917604  2.048308665  0.425881902  1.271337171 -0.0556553306
## 1084 -0.89748826  0.786027181 -2.188082361 -0.097864496 -0.6318971960
## 1091  0.32892044  1.740639547  1.224415767 -0.224524436 -0.1358199080
## 1092 -0.19654835 -0.925993525  0.317344293 -0.662871492  0.2331007588
## 1102 -0.46162870  0.770502287  0.716929013  0.203057096  0.2105954423
## 1103 -1.05468206 -0.570884667  0.290693761  0.435243726  0.6376540939
## 1113 -0.53766568  0.911348651 -2.274236278  0.859954822 -0.4218320913
## 1114 -1.08654649  1.014537567  0.886917502  1.336664101 -0.0710198781
## 1117  3.94985233 -1.716359994 -0.641719964 -0.264276341  0.8567586597
## 1119 -1.02607514 -0.978030272  0.676910859  0.674289447  0.3920284395
## 1123 -0.40290712  0.785648739  1.155943955 -0.021246431 -1.1691012573
## 1125  0.51105853 -0.245840001  0.195980399  0.377499738  0.4724647807
## 1128 -1.31409528 -0.319871405  0.676900918  0.538684115  1.3296487361
## 1138 -0.85701556 -0.402144768  1.015452290 -1.801337794  0.8906035407
## 1139  1.68782662 -1.556740290 -0.300103991  0.269823635 -0.4689481934
## 1150 -0.47890333 -0.235324855  0.744283560  0.211736984  0.1442438079
## 1153 -0.99029732  0.006418909  0.900894666 -0.485086716  1.3897314717
## 1155  3.27981020 -0.122455337 -0.079720740 -0.383851203  1.3578370392
## 1156 -0.26447142 -0.945587037  0.202679447 -0.215468234 -0.7088216703
## 1161  0.29218650 -0.859800419 -0.163904973 -0.497450969 -0.0356847783
## 1167  2.38340587 -0.906554973 -0.249745832  1.453664169  0.8414983923
## 1169 -0.74948837 -0.055476018  0.988541854 -0.407129342  0.4341339074
## 1171 -1.16193265 -0.153610151  0.616256544  0.187084939  1.6029160458
## 1172 -0.85234999  1.046496461 -1.818114337 -0.650465653 -1.8658661054
## 1187 -0.37330855 -0.836688899 -2.926665534  1.099408122  1.3393923955
## 1196  1.97449387  0.724870438  0.154980237  0.521648683 -0.0070421073
## 1200 -0.85470449  0.078257045  0.617160132 -1.082064111  0.0826835327
## 1201 -0.90848917 -0.512845396 -0.052551044  0.118554379 -0.2771893608
## 1202 -0.55881989  0.733094607 -1.906948332 -0.426831779  1.3579036478
## 1211 -0.71135786 -1.113795382  0.469933212 -0.487163002 -0.7658725831
## 1219  1.00211827 -0.527787938  0.094957403  0.341964203  0.3444357469
## 1220 -2.36958769  1.318793961  0.664422393  0.950191016  1.3745582556
## 1244  0.63686737 -0.072893854 -0.004184601  0.861099887 -0.3271630301
## 1245 -0.09223212 -0.394525109  0.632826399  2.006330322 -0.1233382652
## 1253 -0.42348838 -1.659621429 -0.012599247  1.163239747  0.9215912625
## 1254 -1.65405755  2.258022915  0.977681614  0.356666380  0.5496384464
## 1260 -0.52936713 -0.217004991  0.548776249 -0.106260244  0.7882381696
## 1266 -1.48925268  1.112994231  0.791362009  0.181870519  0.2030315648
## 1270 -0.01095539 -1.711741310 -0.095184057  0.131911504 -0.7006242109
## 1271 -0.79148066  0.745969303  0.445003428 -0.163262203  1.2030869534
## 1273 -0.35069960 -0.592198096  0.190379744 -0.364690824 -0.1099135763
## 1276  1.98413790 -0.309127205  0.099063479  0.208938919 -1.2186355928
## 1283 -1.60791374  0.934246935  0.682150296  1.311509022 -0.2133775823
## 1292 -0.07133452  0.476915382 -2.112324648  0.051305163 -0.2223116484
## 1304 -0.02498823  1.749196433  0.420815301  0.371476950 -0.6521043908
## 1308 -0.67872200  0.165448623  0.913062389  1.437175539 -0.5555965173
## 1311  2.90171492 -1.014307999 -0.307250180 -0.210209142 -1.2901585610
## 1313 -0.20083824 -0.963824992 -2.447456872  1.493647219  0.1156611242
## 1330 -0.83945069  0.307354094  0.773393347 -0.468190072 -0.0783363579
## 1331  2.15001966  1.974358369  0.743969906  0.462189144  0.4449896958
## 1334  0.10491643  0.894574891 -2.559751834  0.023052782 -0.7523249302
## 1340 -0.93987414  0.969687358 -1.744902764 -0.159899755  0.7404762311
## 1345 -1.03495768  0.618041754  0.511119055  1.270974152 -0.5198447590
## 1347  0.71576110 -1.572276548 -0.023967718 -2.758394977 -0.3976254910
## 1355  0.28733231 -1.906936971 -3.363334478 -2.593574367 -1.9850384612
## 1358  0.33265796  2.419464057  0.683745576  1.301228864 -0.4859515045
## 1360  0.04748913  1.016177087  0.675830244 -1.293325367  1.2981447013
## 1362 -0.71901647 -1.225017103  0.450688514  0.523935923  1.1415258202
## 1364 -0.01661860 -0.765553826  0.561731922  0.285310986  0.2949393535
## 1366 -0.86284507 -0.324519745 -2.135698875 -0.243419508 -0.4409514021
## 1371 -1.00178822  0.331984988 -0.028255561  0.712416255 -1.0260555598
## 1377 -0.23889689 -1.032796573  0.081468063 -0.221637330 -0.2251706609
## 1380 -0.50449543 -0.429782385 -1.977405358 -0.199835627 -0.2750240893
## 1387 -0.71464969  0.222376085  1.112701563  0.929106095 -0.3663795387
## 1389 -0.56034839 -0.180519831  0.348968514  0.345529963  1.5311545940
## 1390 -0.28870446  0.228248307  0.736748943  1.379959439 -0.3230939241
## 1392 -1.15934931  0.860641899  0.971551179  0.348507151 -1.9697039864
## 1400  0.75672839 -1.052782224  0.198814423 -0.214661527 -1.0352559478
## 1407 -0.68791138  0.476326592  0.031460368 -0.313599967 -2.4720516907
## 1411 -0.26365009  0.440279649  0.585626546  0.048548310 -1.2861282114
## 1417  0.01943097 -1.027251813  0.160513593  1.529878390 -0.3754176159
## 1420 -0.77818757  0.849966001  0.472395659 -0.283078077 -0.5492524925
## 1423 -1.83537770  0.406258795  0.317447876  0.575868695  0.7186816610
## 1430 -1.30144620  0.544123330  0.484187860 -2.677052272 -0.3400302859
## 1434 -0.21417598 -0.139548887  1.116756515 -0.559627990  0.2249108069
## 1435  0.04846469 -2.292120087 -0.403633596 -2.167038749 -1.1917806707
## 1443 -1.78048187  1.380364499 -2.088320240  2.012352403  1.0112815557
## 1445 -1.43648785  1.797500246 -2.704608681 -2.361978302 -1.0441136566
## 1455 -1.20630732  0.589328865  0.032161347 -1.069897300  0.0378960737
## 1462  1.34429149  0.595312143 -2.758826337 -1.088343131 -0.7786121171
## 1463  1.88928554 -0.420583916  0.449550416 -2.883713691  0.6184707331
## 1467  0.44730610  1.788808018  0.799554435 -0.474161278 -0.6278729056
## 1468 -0.09309528 -0.006137157  0.924846250  1.123047993  0.0146421166
## 1470 -0.43010057 -0.906359633  0.294960226  0.851976958 -0.2990289650
##               LD6          LD7          LD8          LD9
## 4     1.055790937  0.491458942 -0.524857751  0.153641184
## 5    -1.559413505 -1.343932045  0.463923580  0.673128280
## 9    -0.360148209  0.940561487 -1.095300797 -0.596338928
## 15   -1.065557024 -0.124321025 -0.743828381 -1.074279216
## 20    1.060563933 -0.876213292 -1.025293345  0.893321045
## 23   -1.010423046  0.153430266  1.373416198 -0.715065753
## 28    0.454209851  0.673846070 -0.238634904 -0.322186902
## 29   -0.239514204 -1.849457800  0.825180802 -0.091361065
## 31    0.513617276 -0.962785145 -0.190907682  0.794558423
## 34    0.103842560 -0.439778373 -1.485136934  1.572424092
## 44   -0.086461189  0.929176278 -0.384398500  0.123330339
## 45    0.117749027 -0.067736236  0.284514872  1.608446733
## 59    1.552301595 -0.103187417  0.049874461 -0.580549909
## 64   -0.163500918 -1.112153778 -0.278541339 -1.989020820
## 66    0.826201305  0.061274393 -1.231165152  0.670128617
## 68   -0.390029121  0.466117913  0.047960603 -0.155555440
## 75    0.016782956 -1.209634792  0.307857163  0.582600795
## 86    2.331132325 -0.828748370 -0.842849373  0.576393341
## 93    0.505644846  1.256896164  0.790172201  0.339320490
## 96    1.777567257 -2.388176685  1.453536845 -1.227032239
## 104  -0.422812138 -0.722399275  1.191397739 -0.302114133
## 113  -0.140689021 -0.296490328 -1.658843686 -0.415061709
## 114  -1.741692104  0.638038302  0.494628129  0.567897432
## 117  -0.487535103  1.200157098 -0.092718237 -0.263984050
## 122  -2.036019649  1.035161829 -1.207720074  0.099792559
## 123   0.196574255 -1.778248234 -1.119332231 -0.962482870
## 124  -0.892845859 -2.071098498  0.317794717 -0.030250203
## 128  -0.539658557  1.901692064  0.115855848 -0.007698423
## 129  -0.466713584  0.488427142  0.553499944  2.035810071
## 134  -0.463649264 -0.009646705 -0.547412425  1.391949026
## 136  -0.685023638 -0.625517922 -0.153821374  0.322549014
## 139  -2.453792011 -0.364139101  0.703406749 -1.682280335
## 140   1.612631887  0.556318905  1.658302742 -0.441423952
## 144  -0.479817796 -0.210076019  1.563172419 -1.086756096
## 152   0.709393894  0.474593749  0.138522054 -0.697145381
## 154   1.710536180 -1.007586678  0.644529222 -1.283577510
## 155  -0.583047246 -0.552526603  0.738045669  0.385013108
## 160   0.680615735 -1.044276417 -0.500518948 -0.228170158
## 173   1.382334854  0.797894035 -0.378867625  0.457242019
## 174  -0.347652389  1.393032956 -0.196432484 -0.411882909
## 177  -0.285333049 -0.333805647 -0.463817814  1.583759837
## 183  -0.214938867  0.877870144  0.677616470 -0.347096015
## 186   0.110817167  1.218272262 -0.991145761 -0.322376204
## 194   0.296964700 -1.036873315 -2.003087901  1.240867578
## 196  -0.204758586  1.097792169  0.519978448 -1.631938202
## 198  -0.554199544  0.046116539 -0.909470938  0.092729023
## 199   0.975616753 -1.310887961 -1.457303617 -0.377568272
## 200   1.351762433  0.208878225 -0.193860768 -1.840920034
## 205  -2.395171272  0.212135772 -0.932243267 -0.873428683
## 209   2.962630837 -1.560327194 -0.250864322 -2.021796167
## 214   1.764124582 -0.491873633  1.099134804 -1.595952311
## 217  -0.468000906  1.058105117 -0.157393419 -2.884942333
## 220   1.288780956  0.957526476 -1.396336271  0.597677473
## 221  -0.758225308 -0.454970689 -2.243128336  0.818547686
## 229  -0.664237267  0.029539092 -0.524933146  1.218515441
## 231   2.161451120 -1.878628658 -0.386920169  0.580654606
## 239  -0.216076054  0.729742290 -0.137917457  0.789487452
## 241   0.942300853 -1.401035549 -0.737132492 -0.106424387
## 245   0.200528639 -0.132400539  0.321815263  1.200519511
## 251  -1.285210958 -1.340039370  0.720103983 -0.216008093
## 257   1.021136537  1.649669681 -0.842810928  0.580899936
## 258  -1.338576218 -0.140585597  1.553535965  1.151047065
## 260  -2.447979640  1.362517790 -1.227808335 -0.196232674
## 270   0.902411604  0.265218345 -0.551765677  0.982694325
## 278  -1.143834679  0.530691566  0.854207041  0.344003843
## 279   1.545427565  1.460415484  1.791873786 -0.630177797
## 286   1.245024462 -0.023839395 -0.556905654  1.307034155
## 287   1.802020288  0.774147212 -0.152867800 -1.338478016
## 290   0.137940067  0.423437214 -0.501257130  1.141022005
## 301   0.568000085  1.029448520 -0.495918634 -0.098670967
## 305   1.362350064  0.093578357  0.997631689  0.767947932
## 307   1.255986562  0.964636620  0.133322613 -0.065573889
## 310   0.479389400 -0.132427977  0.304201502  0.213661613
## 313   2.497162299  0.282257838  1.794562881 -0.441441614
## 316   0.920716473 -0.473642561 -0.297223452  0.218030791
## 319   0.751834192  1.150338607  0.810486622 -0.361012277
## 326  -0.558914420  0.551549451  0.102345652  0.821591578
## 329   0.452792726 -0.843346249  1.031996876 -0.272651332
## 336   0.806018707 -0.671274512  1.263415437  1.192925508
## 338   0.088913562 -0.628580910  0.840309849 -0.788956435
## 340  -0.638016013  0.441932713  0.707058492 -0.869771440
## 342  -0.639617999  0.139260831 -0.134707123  0.753111038
## 343   1.095163848 -0.061872000  0.904399938 -0.513962070
## 347   0.594604725 -0.061864642 -1.459204265 -0.012434944
## 350   1.417467018  1.004545382  0.372746334  0.230688674
## 351   0.311180219  0.475379892 -0.145529835  2.277682820
## 352   0.266995364  0.762511027  0.027877717  0.446120667
## 357   0.123436254 -1.883645075  0.968627862  0.281750294
## 359   1.422153298 -0.852212311 -0.699219049 -0.257381639
## 364   0.558917869  0.929057034 -0.404463669  0.821799575
## 367  -0.801097010  0.112662617  1.263207631  0.465486136
## 368   0.806879861 -1.258145894 -1.619646375  0.428034558
## 373  -0.063514144 -1.078185854 -1.067470273 -1.325209239
## 380   0.724238886 -0.875377377 -0.312952019  1.276480637
## 381  -0.658841406  0.562691045 -1.161262029 -0.160031979
## 383  -0.888167631  2.258528322  0.403119963  1.408331544
## 386   0.070183046 -1.670055754 -0.514745121  0.368482691
## 395   0.774059657  1.578205513  1.886050702 -0.652626163
## 397   0.695070299 -0.784082579 -0.702112342 -0.297870229
## 399  -0.556482349 -0.873128512 -0.338961521 -2.274651678
## 400   0.296859190  1.864856267 -0.610198124  0.884550444
## 401  -1.190477121  0.217900482  0.874224717  1.794924168
## 405  -1.200183419  1.660894904 -0.387301998 -0.469175616
## 410  -1.753900703 -0.748380934  0.008905798 -0.623351320
## 413   0.950375270  0.003262222 -0.200099440 -0.632488345
## 419   0.073527299 -0.362648096  2.324756324 -1.726995561
## 422  -1.556981832 -0.133753761 -1.538900816 -2.161976740
## 423  -2.192520057 -0.565002971  1.254994062  1.784360009
## 428  -1.269236515 -0.073212386 -2.651929371 -0.913526005
## 429  -0.127303112 -2.192351063  0.493381583  1.481939565
## 431  -0.135134027  0.922141307 -1.097414394 -0.503073157
## 435  -2.034658163  1.029369980 -0.742432078  1.414314480
## 436  -2.943436527 -0.890173963 -0.717341521  0.899737886
## 439  -0.108438201  0.087743636 -1.264284202 -0.469182204
## 441  -1.963295721 -0.373448571 -0.700347005 -1.978070372
## 446  -0.662796744 -1.063407120  0.155788486 -1.891529647
## 447   0.354414002 -1.161334684 -1.578426439  0.787143626
## 453   0.288455554  0.846948062 -1.531732447  1.361553525
## 465  -0.839463065 -1.633984109 -0.283009546  1.256944843
## 466  -0.828666563 -1.077428685  0.752282157  0.056172771
## 468  -0.803933019 -0.189514780  1.023196763 -0.802324452
## 470   0.249362517 -0.633920013 -1.285224545 -0.856446719
## 472  -0.202675699 -0.182840925 -0.394421085  0.007713399
## 477  -0.688467651  1.611731805 -0.847898615 -0.165438343
## 479  -1.423716634  0.356421275  0.499701745  0.884278552
## 484  -1.728918783 -1.553445372  0.189069336 -0.384381126
## 494  -0.707938042 -1.881008063  0.012365345  0.507618948
## 495  -0.122338507  0.249279984 -0.353799999 -0.081917377
## 502   0.273197778  0.290463828  0.123848727  0.613466471
## 509   0.066564414 -0.831067124  0.677782352  0.053242659
## 513  -0.281965208 -0.908455988  1.628679936  0.150914198
## 515  -0.895083881  0.743724304  1.328187536  0.152111298
## 518  -0.062541627  1.656603955 -0.377182470 -0.059730504
## 519   1.168742026  0.086326607 -0.602080516  0.347703651
## 534   0.495787838  0.636993871 -1.220957387 -0.856175225
## 538   0.145526920  2.372851204  0.100885339 -0.451600620
## 544  -1.089089155 -0.988905792  0.116196434 -0.794338608
## 548  -0.233284397 -0.733514059 -1.113887147 -0.438789525
## 549   0.507482748 -0.460114492 -1.318385525  0.202058467
## 552   1.898717284 -0.608199547  0.418685904 -1.094866651
## 556   0.154109376  1.297339924 -0.744070134 -0.131939695
## 559  -1.313248543 -1.090003491  0.744480650 -1.374374424
## 560   3.251312551 -0.401839472  0.262491699 -1.573162690
## 562  -0.449097552  0.631346480 -1.049525511  0.198102609
## 564  -0.892101743  0.618396273  0.364357063 -0.222204694
## 567  -1.275790721 -0.597774118 -0.648176658 -0.260821703
## 572  -0.964668878 -1.208894360  1.395192063  1.175218242
## 575   0.451423653 -1.106383095  0.680040712  0.367695163
## 580   0.381664757  1.126096859 -0.033195436 -0.426738203
## 582   0.654404517  0.291650852 -0.591599552  0.634110516
## 583   0.251256154  0.723433873 -0.204050732  1.223852382
## 585   0.190405784 -0.421261413  1.375567949  0.015260095
## 587  -0.469924983  1.022572781  0.056422157 -0.277227469
## 591  -1.209585383  0.383289692 -0.477091736  0.761038012
## 597   1.235369971 -0.012229045 -0.755916478  0.191939189
## 598   0.824201731 -1.670920966 -1.540738959  1.298582276
## 599   1.021263997 -0.325358979  0.676537636 -0.674261746
## 600  -0.140090816  0.061030056 -0.803933940 -0.485504091
## 602  -0.754388030 -1.905923829  0.117870000 -1.284938695
## 604   0.580633413 -0.530621235  0.289075357  1.004418386
## 608  -0.450113325 -0.560437570 -1.037832616  1.390127579
## 616   1.580592463  0.485106013  0.403663855  0.448725926
## 622   0.714455323 -0.369358661  1.470847700  1.193782064
## 629   0.332919010 -0.134222476 -1.333357816 -0.991753221
## 631   1.777347087 -0.035273037  0.837641208  0.129094617
## 632   1.038618427 -1.526631141  1.443894665 -0.394133961
## 633  -0.058148273 -1.545545519 -0.037528491  2.074869546
## 634  -0.802159672  0.603307965  0.942131655 -0.236213355
## 639  -1.813935227  1.578027091 -0.617630090  1.449656228
## 643  -0.241200902  0.449986066  0.332585707  0.098154000
## 644   1.622950026 -0.486970144  0.505330281  0.620665272
## 651   2.133959736 -0.538235067 -0.276384613  0.695007236
## 652   0.836156354 -0.298480002 -0.159205863  2.062181685
## 655   0.977818457 -1.528258990 -1.362397602  0.645848722
## 661   2.197960369 -1.503131919 -1.258601153  2.077896578
## 663   0.609385130  1.073514913  1.406378071  0.174745268
## 665   0.207713540  0.479174383  0.536653397  1.010576009
## 672  -0.440515354  0.332134882  0.291586469 -0.146683370
## 673  -0.352427452 -1.052632214 -1.214770372  0.161552316
## 676  -0.950675636 -0.933627662 -0.353942541 -0.040796092
## 687   0.613233261  1.304445713 -1.115755644  0.058839273
## 693  -0.769832088  0.993216783 -0.667444306 -0.140848866
## 704   0.210350812 -0.351944400 -0.198913147  0.540898172
## 711  -0.775827035  0.969801646 -0.657550586 -0.531675893
## 713  -1.041106600 -0.794545447  0.129570253  1.191761918
## 714   1.840146872 -0.814269191 -1.003759904  0.749730908
## 717  -2.276173654 -0.941223064  0.369952542  0.362368883
## 718  -0.560973253 -0.890443554 -1.138196086 -1.971203294
## 728  -0.879741589 -0.185890747  1.058018707  0.980749355
## 730   0.055967902  0.509727385  0.189556235 -2.053186986
## 734   0.218323610  0.484372992 -0.186870325  1.478734774
## 739   0.163608450  0.400600827 -0.411120929  2.358591865
## 740  -0.360874861 -0.874839265  1.715192205  0.181303795
## 745   0.332509776 -0.073352639  2.014525036 -0.702436708
## 748   0.215159525 -2.435171503 -0.097339661 -0.238337443
## 759   2.269593547 -1.088946611  1.383089427  1.074506401
## 761   0.909600364  0.068920895 -0.619743303  0.823311059
## 763  -1.180112740 -0.173965993  0.989087698 -0.353969267
## 766   0.833875110 -0.489563243 -0.308726086  0.045036298
## 768   1.599839413  0.878045489 -0.223035362 -0.071904845
## 769  -0.181629503  1.541397501 -0.221691686 -1.927817833
## 775  -1.182034011 -0.318321153 -1.863569341  1.653537114
## 780  -0.545990847 -2.913397409 -0.740796028  0.338893498
## 782  -1.297878277  0.794929245  1.390336462  0.488317030
## 794  -0.669351050 -0.034807126  1.689249973 -0.315197170
## 800  -0.142092670  2.063147090 -0.499392324  0.893816214
## 804   0.771864215 -0.904723553 -0.105765191  0.222692642
## 805   0.741423195 -1.421379545  1.893873444 -0.051908816
## 807   0.202605079 -1.460984718 -0.616927080 -0.713182900
## 808   0.188374483  0.300671998 -0.058776709 -0.322132925
## 812   0.287986149 -0.049461118 -1.337982874  0.687911076
## 815  -1.724796968  0.156377449 -0.846947404  0.208313532
## 818  -0.993361539 -1.402163360  0.765193789 -0.966194224
## 822   0.716269494 -0.286353019 -1.578082309 -0.679434592
## 830  -1.192392615  0.933892521  1.387096528 -0.890385347
## 834   0.379098611  0.808143610 -0.469799925  0.385482072
## 835  -0.152689935  0.389806191  1.158606460  0.887011832
## 838   0.336646854 -1.794088823  0.340227799 -1.570375221
## 841   1.195755904 -0.664050539 -1.098445220 -0.053367397
## 842  -0.979260510  0.020052741 -1.802693283 -1.881736632
## 844  -0.486339857 -1.054744488  1.606210397 -0.004376197
## 847  -0.951255795  0.372063491 -0.706827941  0.747658726
## 848   0.540948441  1.910478346 -0.490298579  0.387525671
## 852   0.739931376  0.582302919 -1.348013485 -0.455650522
## 853  -0.819765225 -0.297370820  0.703534330  1.762361184
## 854  -1.095282229  1.826748676  0.111711844 -0.094152829
## 856   1.858553343  0.288227121  0.271473530  0.767948546
## 857  -0.213035028 -0.011364594  2.384131331 -0.280046666
## 858   0.661444978  0.101973840 -0.288459795  0.075531263
## 861   0.154450717  0.349466379  0.819427198  0.366297781
## 865   0.824896724  0.049280230  1.836297022 -0.483289826
## 871  -0.629565421  0.828944246 -0.672736036 -1.734840450
## 879   0.351557450 -0.318644921 -2.207894867 -0.818001005
## 882   0.336667946  0.192234238 -0.797047498  1.110300471
## 889   0.438199605 -0.465691194  0.436562733  0.409852270
## 890  -0.656591622  0.895981843  1.634161655 -1.445154463
## 892  -0.284847608 -1.157801606  0.935856029  2.394437726
## 898   1.482563256 -1.830969888 -1.089894918  1.280123751
## 915   0.237287898  1.071625986 -1.272418621  1.689993659
## 927   0.256767233 -0.836287358 -1.566568376  0.784347324
## 939  -0.025810278 -1.326654143 -0.186720005 -0.841418481
## 942  -0.719384424 -0.783286469  1.472442144  0.565952913
## 947  -0.364879611  1.123050152 -1.292958377 -1.522788360
## 949  -1.418267926  1.036646606  0.381521464 -1.834195088
## 950  -1.304226879 -0.294273861  0.690956196  0.256294556
## 957   0.648257113 -0.358564619 -1.637078822 -0.619034712
## 959   1.218979940  0.664114295  0.263233096  0.156505826
## 962   0.597779886  0.054228718  0.012017479  0.032594567
## 963   0.301639319  0.470937051 -0.384546044  0.513247786
## 964  -0.585306972  0.507681945  0.226648414  0.589568810
## 965  -1.788028717  1.281140632 -1.193464559  0.260569838
## 970   1.258940142 -0.203151012 -0.861088944  1.273327993
## 973  -0.469601384  0.248390606 -0.692155115  1.266851993
## 977   0.034677961  0.184657610 -2.089216836 -0.811757525
## 986   0.564028224  1.222850268 -0.074738553 -1.576000226
## 991  -1.953129985 -1.601966863 -0.503619088  1.848954470
## 995   0.375627195  0.600926227 -1.139087950 -0.676922772
## 998  -0.017232348  1.002966026 -0.597672332 -0.794159117
## 1000 -0.639017456  1.533500957 -0.159265701 -0.343174444
## 1003 -0.836806258 -0.233315119 -0.416293550  0.331464201
## 1007 -1.774069046  0.172197056 -0.229818325 -0.806885981
## 1008 -1.169788215  0.735523360  0.272993108  1.472249059
## 1014  0.236477808  0.385716505 -1.335799574 -1.324379592
## 1016  0.861909062  0.645064816 -1.082800823 -0.584988360
## 1017 -1.853635538  0.026542582  0.526183117  0.521564758
## 1025 -1.262740948 -1.541726947  0.270845395  0.385323563
## 1029  1.653890919 -0.679356839  0.973256743 -1.055728879
## 1032 -1.528061813 -1.917886952  0.046484975  1.004366896
## 1035 -1.106722822  0.555357030 -0.354325956 -1.113512840
## 1040 -0.578258551 -0.459872104  1.255257195 -0.268222130
## 1043  0.716762842 -0.491094853 -0.581317295  0.654726582
## 1052  1.324575778 -2.226087020  1.115071336 -1.231551282
## 1053  0.992031690  0.531586092  0.693374021 -0.115122386
## 1056 -0.945382338  0.092359236  0.469273192 -2.036225539
## 1058  0.079138388  0.027427752  2.250415583 -1.678860418
## 1060  0.159309518  0.883077761 -0.809743699  1.730097353
## 1062 -0.482880742  1.588783887 -0.717927051  0.124493518
## 1064 -0.959121886  0.519321029 -0.213624965 -0.690462978
## 1065 -0.478643591  0.261001289 -0.419942261  1.297135936
## 1067 -0.569197247 -1.707311870  0.407155557 -1.036688219
## 1068  1.191223598 -0.264847008 -0.216852000 -0.396901984
## 1071 -0.429361456  1.685042747  0.089602244 -0.272548571
## 1072  0.397282019  0.373398915 -0.916870999  0.843781571
## 1080 -0.441161112 -0.358565604  0.085822500 -0.097045697
## 1081 -0.978292848 -1.102880039 -1.604336544  0.347463807
## 1084  2.446186484  1.690990621  0.320854239 -1.517449895
## 1091 -1.317748094  1.390866041 -0.244929481  0.541207002
## 1092 -0.531678993  1.304673644 -1.316591911 -1.144605121
## 1102  0.021555411  0.966196220 -0.835594550  0.673614876
## 1103  1.804664384 -0.735996011  0.577690177 -0.101539736
## 1113  0.214153613  0.280119579 -0.223085620  0.518890806
## 1114  1.594678383  1.168881968 -0.159291362 -1.031586308
## 1117 -0.085329059 -0.768809277 -0.871272183 -1.626013234
## 1119 -0.619702587 -0.952296045  1.522690989  0.641221794
## 1123 -1.157351451  1.294606981  0.622591735  1.086679758
## 1125  0.575937280  0.368431442 -0.820522186  0.512770342
## 1128  0.004649243  0.713828864 -0.599595057 -0.083570051
## 1138 -1.110332834  0.609504610  0.929284966 -1.202185331
## 1139 -0.092332153 -0.915371439 -0.304656073 -1.614838553
## 1150 -0.623595948  1.957536118 -1.008383226 -1.154376550
## 1153 -0.715887227  0.326312455  0.388202887  1.698407834
## 1155 -0.476640326  0.101177765 -1.540656010 -1.616894126
## 1156  0.373977588  0.424208367 -0.049189048  1.518108241
## 1161  1.074051090 -0.025819727 -0.778280494  1.978739901
## 1167  0.934027348 -0.989897413 -0.142717586 -0.227238268
## 1169 -1.307481848 -0.583951261  1.608914435  1.828748901
## 1171  1.560873837  0.279584745  0.345987750  0.420732926
## 1172  1.002434117  0.590955627  2.165310981 -1.005635339
## 1187 -0.304747751 -0.394048063 -1.503721795  0.313527674
## 1196  0.406721416 -0.645831524 -0.419518549  0.759425589
## 1200 -0.582209234 -1.505417448  0.641040049 -2.572464823
## 1201  1.027941374 -1.254083436 -0.487339629  1.146021444
## 1202 -0.663468888  1.525719153 -0.212166683  1.518972692
## 1211 -1.037753136  0.418118105 -0.040165915 -0.966059467
## 1219  0.626637223  0.547880810 -0.746801703  0.630185777
## 1220  0.423330324 -1.093337037 -1.492844470 -1.053040575
## 1244 -0.466011897 -0.855970734 -1.252018336  1.000070472
## 1245  0.601974545  1.873092037 -0.380767574 -0.384388255
## 1253  1.299678055  0.148710340 -0.337538472  0.622332162
## 1254  1.314097938 -0.079180428 -0.599207565 -0.542914104
## 1260 -0.602801463 -0.014708877 -0.451697337 -0.550958610
## 1266  1.391948398  0.541522738 -0.380129468 -0.397016036
## 1270  0.563236968 -0.764494303  0.568279517  1.297524345
## 1271  0.430770630 -0.580622518 -0.906990184  1.275606409
## 1273  0.543261886  0.674983446 -0.813675933  1.256629882
## 1276 -0.273008275 -1.122630321  0.820487852  0.725135062
## 1283  0.439112124  0.496244747 -1.391320173 -1.201997129
## 1292  2.164775008  2.248468499  0.660383958 -1.544530309
## 1304  0.259357480 -1.002339405 -1.100946740 -0.034122376
## 1308 -0.070179775  1.414016648  0.143849227  0.101256465
## 1311 -0.436424094 -1.345624467  0.294250325 -0.604523266
## 1313  0.111874055  2.034056940 -0.751221860 -1.861953425
## 1330 -0.221288816  1.574198137 -0.650858957  1.347671653
## 1331 -1.251998504 -1.856628928  0.566331266 -0.240406006
## 1334  0.018434276 -0.066317780 -0.791644605  0.025260215
## 1340 -0.700981382  2.046973116 -0.257790105  1.306211167
## 1345  0.623655960  0.618556791 -1.344197678 -0.961931169
## 1347 -0.036540900 -0.275388871  0.498531250 -0.206529314
## 1355 -0.722288805 -1.217205130  0.083757789  0.728041641
## 1358 -1.268959616 -0.725823315 -1.842494716 -0.283400254
## 1360  0.942742358  0.266810402  0.063985057  1.547399670
## 1362  0.061348867  0.112461829  0.347177069  0.652583117
## 1364  0.582963353 -0.015417839  1.228710118 -1.009030514
## 1366 -1.154244316  1.748038676 -0.495777349 -1.270661109
## 1371 -0.551561214 -1.414817069 -2.246688314 -0.806279856
## 1377 -1.269420710 -1.090970439 -0.447126781  1.526465743
## 1380 -1.961192147  0.472390395  0.950120355 -1.079845705
## 1387  0.769824223  1.905447960  1.022903837 -0.310701056
## 1389 -0.174238974 -1.152438381 -0.573537592 -0.932032638
## 1390  0.405052789  1.770009129 -0.516244685  0.230821972
## 1392  0.408055696 -0.107880774  1.396235494 -0.477867324
## 1400 -0.691489044 -0.747263722  0.782871635  0.126276900
## 1407  0.534229116 -0.307404037 -1.513016062 -0.287989894
## 1411 -0.290348857 -0.094787900  0.206889856  0.953141232
## 1417  1.182081914  1.114788167 -0.539672478  0.197780118
## 1420  1.089843185  0.579970400 -1.228464224 -2.181961496
## 1423  0.653833020 -0.819499664 -1.531435284 -0.864730961
## 1430 -1.847283694 -2.162527525 -0.255642502  0.136500523
## 1434 -0.598621696  0.273341645  2.193545001  0.141013185
## 1435  0.316933196 -1.620169135  0.513631976 -1.706607116
## 1443 -1.413436766 -2.817448167  0.181669275  0.212198300
## 1445  2.889123930 -0.590958350 -0.575466816  0.405022842
## 1455  0.243190208 -1.075142354 -2.228413731 -0.771456186
## 1462 -0.599340002  1.138538065 -1.987256430 -1.359580137
## 1463 -0.896940690  0.135918291  0.844945217  0.189488183
## 1467 -0.371715456  1.310229525 -1.199439044  0.939483906
## 1468 -0.706467187  0.563918463  0.811828553  0.020315514
## 1470 -1.240034623 -0.612341309 -0.344309854  0.611334554

# Get the posteriors as a dataframe.
attr_raw.lda.predict.posteriors <- as.data.frame(attr_raw.lda.predict$posterior)
# Map numeric values to categorical labels
test_raw.df$Attrition <- ifelse(test_raw.df$Attrition == 0, "No", "Yes")

pred <- prediction(attr_raw.lda.predict.posteriors[,5], test_raw.df$Attrition)

roc.perf = performance(pred, measure = "tpr", x.measure = "fpr")
auc.train <- performance(pred, measure = "auc")
auc.train <- auc.train@y.values
plot(roc.perf)
abline(a=0, b= 1)
text(x = .25, y = .65 ,paste("AUC = ", round(auc.train[[1]],3), sep = ""))

#Inference: #Lower AUC score indicates model performance is not good.

# Iris LDA
data("iris")
iris

##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1            5.1         3.5          1.4         0.2     setosa
## 2            4.9         3.0          1.4         0.2     setosa
## 3            4.7         3.2          1.3         0.2     setosa
## 4            4.6         3.1          1.5         0.2     setosa
## 5            5.0         3.6          1.4         0.2     setosa
## 6            5.4         3.9          1.7         0.4     setosa
## 7            4.6         3.4          1.4         0.3     setosa
## 8            5.0         3.4          1.5         0.2     setosa
## 9            4.4         2.9          1.4         0.2     setosa
## 10           4.9         3.1          1.5         0.1     setosa
## 11           5.4         3.7          1.5         0.2     setosa
## 12           4.8         3.4          1.6         0.2     setosa
## 13           4.8         3.0          1.4         0.1     setosa
## 14           4.3         3.0          1.1         0.1     setosa
## 15           5.8         4.0          1.2         0.2     setosa
## 16           5.7         4.4          1.5         0.4     setosa
## 17           5.4         3.9          1.3         0.4     setosa
## 18           5.1         3.5          1.4         0.3     setosa
## 19           5.7         3.8          1.7         0.3     setosa
## 20           5.1         3.8          1.5         0.3     setosa
## 21           5.4         3.4          1.7         0.2     setosa
## 22           5.1         3.7          1.5         0.4     setosa
## 23           4.6         3.6          1.0         0.2     setosa
## 24           5.1         3.3          1.7         0.5     setosa
## 25           4.8         3.4          1.9         0.2     setosa
## 26           5.0         3.0          1.6         0.2     setosa
## 27           5.0         3.4          1.6         0.4     setosa
## 28           5.2         3.5          1.5         0.2     setosa
## 29           5.2         3.4          1.4         0.2     setosa
## 30           4.7         3.2          1.6         0.2     setosa
## 31           4.8         3.1          1.6         0.2     setosa
## 32           5.4         3.4          1.5         0.4     setosa
## 33           5.2         4.1          1.5         0.1     setosa
## 34           5.5         4.2          1.4         0.2     setosa
## 35           4.9         3.1          1.5         0.2     setosa
## 36           5.0         3.2          1.2         0.2     setosa
## 37           5.5         3.5          1.3         0.2     setosa
## 38           4.9         3.6          1.4         0.1     setosa
## 39           4.4         3.0          1.3         0.2     setosa
## 40           5.1         3.4          1.5         0.2     setosa
## 41           5.0         3.5          1.3         0.3     setosa
## 42           4.5         2.3          1.3         0.3     setosa
## 43           4.4         3.2          1.3         0.2     setosa
## 44           5.0         3.5          1.6         0.6     setosa
## 45           5.1         3.8          1.9         0.4     setosa
## 46           4.8         3.0          1.4         0.3     setosa
## 47           5.1         3.8          1.6         0.2     setosa
## 48           4.6         3.2          1.4         0.2     setosa
## 49           5.3         3.7          1.5         0.2     setosa
## 50           5.0         3.3          1.4         0.2     setosa
## 51           7.0         3.2          4.7         1.4 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 53           6.9         3.1          4.9         1.5 versicolor
## 54           5.5         2.3          4.0         1.3 versicolor
## 55           6.5         2.8          4.6         1.5 versicolor
## 56           5.7         2.8          4.5         1.3 versicolor
## 57           6.3         3.3          4.7         1.6 versicolor
## 58           4.9         2.4          3.3         1.0 versicolor
## 59           6.6         2.9          4.6         1.3 versicolor
## 60           5.2         2.7          3.9         1.4 versicolor
## 61           5.0         2.0          3.5         1.0 versicolor
## 62           5.9         3.0          4.2         1.5 versicolor
## 63           6.0         2.2          4.0         1.0 versicolor
## 64           6.1         2.9          4.7         1.4 versicolor
## 65           5.6         2.9          3.6         1.3 versicolor
## 66           6.7         3.1          4.4         1.4 versicolor
## 67           5.6         3.0          4.5         1.5 versicolor
## 68           5.8         2.7          4.1         1.0 versicolor
## 69           6.2         2.2          4.5         1.5 versicolor
## 70           5.6         2.5          3.9         1.1 versicolor
## 71           5.9         3.2          4.8         1.8 versicolor
## 72           6.1         2.8          4.0         1.3 versicolor
## 73           6.3         2.5          4.9         1.5 versicolor
## 74           6.1         2.8          4.7         1.2 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 76           6.6         3.0          4.4         1.4 versicolor
## 77           6.8         2.8          4.8         1.4 versicolor
## 78           6.7         3.0          5.0         1.7 versicolor
## 79           6.0         2.9          4.5         1.5 versicolor
## 80           5.7         2.6          3.5         1.0 versicolor
## 81           5.5         2.4          3.8         1.1 versicolor
## 82           5.5         2.4          3.7         1.0 versicolor
## 83           5.8         2.7          3.9         1.2 versicolor
## 84           6.0         2.7          5.1         1.6 versicolor
## 85           5.4         3.0          4.5         1.5 versicolor
## 86           6.0         3.4          4.5         1.6 versicolor
## 87           6.7         3.1          4.7         1.5 versicolor
## 88           6.3         2.3          4.4         1.3 versicolor
## 89           5.6         3.0          4.1         1.3 versicolor
## 90           5.5         2.5          4.0         1.3 versicolor
## 91           5.5         2.6          4.4         1.2 versicolor
## 92           6.1         3.0          4.6         1.4 versicolor
## 93           5.8         2.6          4.0         1.2 versicolor
## 94           5.0         2.3          3.3         1.0 versicolor
## 95           5.6         2.7          4.2         1.3 versicolor
## 96           5.7         3.0          4.2         1.2 versicolor
## 97           5.7         2.9          4.2         1.3 versicolor
## 98           6.2         2.9          4.3         1.3 versicolor
## 99           5.1         2.5          3.0         1.1 versicolor
## 100          5.7         2.8          4.1         1.3 versicolor
## 101          6.3         3.3          6.0         2.5  virginica
## 102          5.8         2.7          5.1         1.9  virginica
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 105          6.5         3.0          5.8         2.2  virginica
## 106          7.6         3.0          6.6         2.1  virginica
## 107          4.9         2.5          4.5         1.7  virginica
## 108          7.3         2.9          6.3         1.8  virginica
## 109          6.7         2.5          5.8         1.8  virginica
## 110          7.2         3.6          6.1         2.5  virginica
## 111          6.5         3.2          5.1         2.0  virginica
## 112          6.4         2.7          5.3         1.9  virginica
## 113          6.8         3.0          5.5         2.1  virginica
## 114          5.7         2.5          5.0         2.0  virginica
## 115          5.8         2.8          5.1         2.4  virginica
## 116          6.4         3.2          5.3         2.3  virginica
## 117          6.5         3.0          5.5         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 119          7.7         2.6          6.9         2.3  virginica
## 120          6.0         2.2          5.0         1.5  virginica
## 121          6.9         3.2          5.7         2.3  virginica
## 122          5.6         2.8          4.9         2.0  virginica
## 123          7.7         2.8          6.7         2.0  virginica
## 124          6.3         2.7          4.9         1.8  virginica
## 125          6.7         3.3          5.7         2.1  virginica
## 126          7.2         3.2          6.0         1.8  virginica
## 127          6.2         2.8          4.8         1.8  virginica
## 128          6.1         3.0          4.9         1.8  virginica
## 129          6.4         2.8          5.6         2.1  virginica
## 130          7.2         3.0          5.8         1.6  virginica
## 131          7.4         2.8          6.1         1.9  virginica
## 132          7.9         3.8          6.4         2.0  virginica
## 133          6.4         2.8          5.6         2.2  virginica
## 134          6.3         2.8          5.1         1.5  virginica
## 135          6.1         2.6          5.6         1.4  virginica
## 136          7.7         3.0          6.1         2.3  virginica
## 137          6.3         3.4          5.6         2.4  virginica
## 138          6.4         3.1          5.5         1.8  virginica
## 139          6.0         3.0          4.8         1.8  virginica
## 140          6.9         3.1          5.4         2.1  virginica
## 141          6.7         3.1          5.6         2.4  virginica
## 142          6.9         3.1          5.1         2.3  virginica
## 143          5.8         2.7          5.1         1.9  virginica
## 144          6.8         3.2          5.9         2.3  virginica
## 145          6.7         3.3          5.7         2.5  virginica
## 146          6.7         3.0          5.2         2.3  virginica
## 147          6.3         2.5          5.0         1.9  virginica
## 148          6.5         3.0          5.2         2.0  virginica
## 149          6.2         3.4          5.4         2.3  virginica
## 150          5.9         3.0          5.1         1.8  virginica

head(iris, 3)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa

str(iris)

## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

r <- lda(formula = Species ~ ., data = iris)
r

## Call:
## lda(Species ~ ., data = iris)
## 
## Prior probabilities of groups:
##     setosa versicolor  virginica 
##  0.3333333  0.3333333  0.3333333 
## 
## Group means:
##            Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa            5.006       3.428        1.462       0.246
## versicolor        5.936       2.770        4.260       1.326
## virginica         6.588       2.974        5.552       2.026
## 
## Coefficients of linear discriminants:
##                     LD1         LD2
## Sepal.Length  0.8293776 -0.02410215
## Sepal.Width   1.5344731 -2.16452123
## Petal.Length -2.2012117  0.93192121
## Petal.Width  -2.8104603 -2.83918785
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9912 0.0088

summary(r)

##         Length Class  Mode     
## prior    3     -none- numeric  
## counts   3     -none- numeric  
## means   12     -none- numeric  
## scaling  8     -none- numeric  
## lev      3     -none- character
## svd      2     -none- numeric  
## N        1     -none- numeric  
## call     3     -none- call     
## terms    3     terms  call     
## xlevels  0     -none- list

print(r)

## Call:
## lda(Species ~ ., data = iris)
## 
## Prior probabilities of groups:
##     setosa versicolor  virginica 
##  0.3333333  0.3333333  0.3333333 
## 
## Group means:
##            Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa            5.006       3.428        1.462       0.246
## versicolor        5.936       2.770        4.260       1.326
## virginica         6.588       2.974        5.552       2.026
## 
## Coefficients of linear discriminants:
##                     LD1         LD2
## Sepal.Length  0.8293776 -0.02410215
## Sepal.Width   1.5344731 -2.16452123
## Petal.Length -2.2012117  0.93192121
## Petal.Width  -2.8104603 -2.83918785
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9912 0.0088

r$counts

##     setosa versicolor  virginica 
##         50         50         50

r$means

##            Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa            5.006       3.428        1.462       0.246
## versicolor        5.936       2.770        4.260       1.326
## virginica         6.588       2.974        5.552       2.026

r$scaling

##                     LD1         LD2
## Sepal.Length  0.8293776 -0.02410215
## Sepal.Width   1.5344731 -2.16452123
## Petal.Length -2.2012117  0.93192121
## Petal.Width  -2.8104603 -2.83918785

r$prior

##     setosa versicolor  virginica 
##  0.3333333  0.3333333  0.3333333

r$lev

## [1] "setosa"     "versicolor" "virginica"

r$svd

## [1] 48.642644  4.579983

#singular values (svd) that gives the ratio of the between- and within-group standard deviations on the linear discriminant variables.
r$N

## [1] 150

r$call

## lda(formula = Species ~ ., data = iris)

(prop = r$svd^2/sum(r$svd^2))

## [1] 0.991212605 0.008787395

#we can use the singular values to compute the amount of the between-group variance that is explained by each linear discriminant. In our example we see that the first linear discriminant explains more than 99% of the between-group variance in the iris dataset.
r2 <- lda(formula = Species ~ ., data = iris, CV = TRUE)
r2

## $class
##   [1] setosa     setosa     setosa     setosa     setosa     setosa    
##   [7] setosa     setosa     setosa     setosa     setosa     setosa    
##  [13] setosa     setosa     setosa     setosa     setosa     setosa    
##  [19] setosa     setosa     setosa     setosa     setosa     setosa    
##  [25] setosa     setosa     setosa     setosa     setosa     setosa    
##  [31] setosa     setosa     setosa     setosa     setosa     setosa    
##  [37] setosa     setosa     setosa     setosa     setosa     setosa    
##  [43] setosa     setosa     setosa     setosa     setosa     setosa    
##  [49] setosa     setosa     versicolor versicolor versicolor versicolor
##  [55] versicolor versicolor versicolor versicolor versicolor versicolor
##  [61] versicolor versicolor versicolor versicolor versicolor versicolor
##  [67] versicolor versicolor versicolor versicolor virginica  versicolor
##  [73] versicolor versicolor versicolor versicolor versicolor versicolor
##  [79] versicolor versicolor versicolor versicolor versicolor virginica 
##  [85] versicolor versicolor versicolor versicolor versicolor versicolor
##  [91] versicolor versicolor versicolor versicolor versicolor versicolor
##  [97] versicolor versicolor versicolor versicolor virginica  virginica 
## [103] virginica  virginica  virginica  virginica  virginica  virginica 
## [109] virginica  virginica  virginica  virginica  virginica  virginica 
## [115] virginica  virginica  virginica  virginica  virginica  virginica 
## [121] virginica  virginica  virginica  virginica  virginica  virginica 
## [127] virginica  virginica  virginica  virginica  virginica  virginica 
## [133] virginica  versicolor virginica  virginica  virginica  virginica 
## [139] virginica  virginica  virginica  virginica  virginica  virginica 
## [145] virginica  virginica  virginica  virginica  virginica  virginica 
## Levels: setosa versicolor virginica
## 
## $posterior
##           setosa   versicolor    virginica
## 1   1.000000e+00 5.087494e-22 4.385241e-42
## 2   1.000000e+00 9.588256e-18 8.888069e-37
## 3   1.000000e+00 1.983745e-19 8.606982e-39
## 4   1.000000e+00 1.505573e-16 5.101765e-35
## 5   1.000000e+00 2.075670e-22 1.739832e-42
## 6   1.000000e+00 5.332271e-21 8.674906e-40
## 7   1.000000e+00 1.498839e-18 3.999205e-37
## 8   1.000000e+00 5.268133e-20 1.983027e-39
## 9   1.000000e+00 2.280729e-15 1.293376e-33
## 10  1.000000e+00 1.504085e-18 5.037348e-38
## 11  1.000000e+00 1.296140e-23 4.023338e-44
## 12  1.000000e+00 2.171874e-18 3.223111e-37
## 13  1.000000e+00 1.996136e-18 6.109118e-38
## 14  1.000000e+00 1.604055e-19 2.549802e-39
## 15  1.000000e+00 2.843397e-31 1.593594e-54
## 16  1.000000e+00 2.330545e-28 3.074132e-49
## 17  1.000000e+00 5.136116e-25 3.269819e-45
## 18  1.000000e+00 5.747697e-21 2.253825e-40
## 19  1.000000e+00 2.187125e-22 4.069438e-42
## 20  1.000000e+00 3.297882e-22 9.802494e-42
## 21  1.000000e+00 1.757286e-19 8.150916e-39
## 22  1.000000e+00 2.027767e-20 3.730752e-39
## 23  1.000000e+00 5.650696e-25 6.509776e-46
## 24  1.000000e+00 8.618517e-15 7.014744e-32
## 25  1.000000e+00 1.520334e-15 1.857885e-33
## 26  1.000000e+00 2.936141e-16 8.159510e-35
## 27  1.000000e+00 4.557392e-17 5.510803e-35
## 28  1.000000e+00 2.079675e-21 2.831513e-41
## 29  1.000000e+00 1.232321e-21 1.082692e-41
## 30  1.000000e+00 1.153050e-16 4.267126e-35
## 31  1.000000e+00 2.584595e-16 9.537258e-35
## 32  1.000000e+00 2.878754e-19 5.473623e-38
## 33  1.000000e+00 2.247070e-27 4.047137e-49
## 34  1.000000e+00 2.620949e-29 1.970538e-51
## 35  1.000000e+00 1.493279e-17 2.047516e-36
## 36  1.000000e+00 2.146308e-21 1.550216e-41
## 37  1.000000e+00 1.673983e-24 1.322398e-45
## 38  1.000000e+00 3.810942e-23 9.131835e-44
## 39  1.000000e+00 5.423320e-17 1.146137e-35
## 40  1.000000e+00 2.414191e-20 6.552342e-40
## 41  1.000000e+00 1.417602e-21 3.569675e-41
## 42  1.000000e+00 8.956712e-11 4.968454e-28
## 43  1.000000e+00 2.125837e-18 2.395462e-37
## 44  1.000000e+00 1.101293e-15 1.403899e-32
## 45  1.000000e+00 2.285363e-17 5.214629e-35
## 46  1.000000e+00 2.087086e-16 1.027948e-34
## 47  1.000000e+00 2.588201e-22 3.634491e-42
## 48  1.000000e+00 3.643000e-18 4.504970e-37
## 49  1.000000e+00 3.000767e-23 1.346233e-43
## 50  1.000000e+00 3.171862e-20 7.860312e-40
## 51  3.157725e-18 9.998716e-01 1.284247e-04
## 52  1.753919e-19 9.991816e-01 8.184018e-04
## 53  2.551962e-22 9.951044e-01 4.895626e-03
## 54  2.742687e-22 9.995996e-01 4.004477e-04
## 55  4.854978e-23 9.951404e-01 4.859638e-03
## 56  9.575747e-23 9.982973e-01 1.702702e-03
## 57  4.467689e-22 9.838631e-01 1.613691e-02
## 58  5.922943e-14 9.999999e-01 8.584221e-08
## 59  8.088509e-20 9.998655e-01 1.344590e-04
## 60  1.767441e-20 9.994314e-01 5.686054e-04
## 61  3.330661e-18 9.999987e-01 1.314516e-06
## 62  8.331100e-20 9.991631e-01 8.369389e-04
## 63  4.614428e-18 9.999989e-01 1.117671e-06
## 64  1.290071e-23 9.939163e-01 6.083745e-03
## 65  5.229707e-14 9.999984e-01 1.593028e-06
## 66  3.393529e-17 9.999528e-01 4.721492e-05
## 67  7.983370e-24 9.763990e-01 2.360097e-02
## 68  3.119288e-16 9.999991e-01 8.659241e-07
## 69  3.847473e-28 9.390462e-01 6.095377e-02
## 70  1.678698e-17 9.999966e-01 3.360127e-06
## 71  1.302246e-28 1.772727e-01 8.227273e-01
## 72  1.113263e-16 9.999902e-01 9.801197e-06
## 73  1.634947e-29 7.868347e-01 2.131653e-01
## 74  3.331093e-22 9.995073e-01 4.926830e-04
## 75  1.013127e-17 9.999741e-01 2.594176e-05
## 76  2.949236e-18 9.999081e-01 9.193549e-05
## 77  7.224891e-23 9.979459e-01 2.054146e-03
## 78  2.386376e-27 6.569495e-01 3.430505e-01
## 79  4.473658e-23 9.922840e-01 7.716012e-03
## 80  7.145460e-12 1.000000e+00 1.241414e-08
## 81  1.333306e-17 9.999970e-01 3.044209e-06
## 82  1.119894e-15 9.999997e-01 2.916503e-07
## 83  1.748156e-16 9.999961e-01 3.876682e-06
## 84  1.125494e-33 9.924153e-02 9.007585e-01
## 85  1.191672e-24 9.474667e-01 5.253333e-02
## 86  1.983291e-20 9.924721e-01 7.527887e-03
## 87  4.531906e-21 9.980100e-01 1.989996e-03
## 88  2.035626e-23 9.993358e-01 6.642410e-04
## 89  7.813451e-18 9.999440e-01 5.603286e-05
## 90  8.212308e-21 9.998033e-01 1.967487e-04
## 91  6.631189e-23 9.992802e-01 7.197827e-04
## 92  7.049062e-22 9.979525e-01 2.047473e-03
## 93  4.490728e-18 9.999881e-01 1.188058e-05
## 94  2.600275e-14 9.999999e-01 8.745690e-08
## 95  6.422939e-21 9.996751e-01 3.248823e-04
## 96  2.159263e-17 9.999804e-01 1.956029e-05
## 97  3.823305e-19 9.998801e-01 1.199041e-04
## 98  2.089502e-18 9.999504e-01 4.963639e-05
## 99  9.013113e-11 1.000000e+00 9.943306e-09
## 100 6.167377e-19 9.999219e-01 7.813051e-05
## 101 1.335977e-53 3.188548e-09 1.000000e+00
## 102 9.949508e-38 1.209398e-03 9.987906e-01
## 103 1.950796e-42 2.774428e-05 9.999723e-01
## 104 3.081602e-38 1.232592e-03 9.987674e-01
## 105 5.411117e-46 1.807449e-06 9.999982e-01
## 106 5.887455e-50 5.662591e-07 9.999994e-01
## 107 1.203272e-32 8.794800e-02 9.120520e-01
## 108 1.774038e-42 1.735541e-04 9.998264e-01
## 109 1.924345e-42 2.617818e-04 9.997382e-01
## 110 1.851248e-46 1.352651e-07 9.999999e-01
## 111 4.379051e-32 1.446014e-02 9.855399e-01
## 112 2.052671e-37 1.776421e-03 9.982236e-01
## 113 9.704392e-39 2.172029e-04 9.997828e-01
## 114 2.386650e-40 2.251253e-04 9.997749e-01
## 115 8.048237e-46 8.410965e-07 9.999992e-01
## 116 1.008588e-39 2.840103e-05 9.999716e-01
## 117 2.811294e-35 6.595206e-03 9.934048e-01
## 118 7.282186e-45 1.296566e-06 9.999987e-01
## 119 1.004644e-64 2.647509e-10 1.000000e+00
## 120 3.160887e-33 3.033047e-01 6.966953e-01
## 121 1.719583e-42 6.688965e-06 9.999933e-01
## 122 6.252717e-37 9.870164e-04 9.990130e-01
## 123 2.627103e-51 7.704580e-07 9.999992e-01
## 124 1.504499e-31 1.070121e-01 8.929879e-01
## 125 3.688147e-39 9.571422e-05 9.999043e-01
## 126 2.426533e-36 3.398007e-03 9.966020e-01
## 127 3.865436e-30 2.055755e-01 7.944245e-01
## 128 3.606381e-30 1.437670e-01 8.562330e-01
## 129 8.371636e-44 1.376281e-05 9.999862e-01
## 130 2.937738e-32 1.589920e-01 8.410080e-01
## 131 6.294581e-42 1.714027e-04 9.998286e-01
## 132 5.466934e-36 7.736441e-04 9.992264e-01
## 133 1.208158e-45 3.051435e-06 9.999969e-01
## 134 5.464475e-29 7.876238e-01 2.123762e-01
## 135 9.884011e-35 1.578198e-01 8.421802e-01
## 136 6.515088e-46 1.990735e-06 9.999980e-01
## 137 2.840394e-44 7.895048e-07 9.999992e-01
## 138 7.160822e-35 7.053731e-03 9.929463e-01
## 139 1.782247e-29 2.122042e-01 7.877958e-01
## 140 3.640914e-36 9.289807e-04 9.990710e-01
## 141 5.881132e-45 1.108009e-06 9.999989e-01
## 142 2.122304e-35 6.157433e-04 9.993843e-01
## 143 9.949508e-38 1.209398e-03 9.987906e-01
## 144 9.585800e-46 9.978596e-07 9.999990e-01
## 145 2.206003e-46 2.038879e-07 9.999998e-01
## 146 1.133074e-38 8.851900e-05 9.999115e-01
## 147 8.781586e-36 7.084468e-03 9.929155e-01
## 148 7.108984e-35 3.342993e-03 9.966570e-01
## 149 3.096565e-40 1.338572e-05 9.999866e-01
## 150 3.585667e-33 2.058806e-02 9.794119e-01
## 
## $terms
## Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width
## attr(,"variables")
## list(Species, Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)
## attr(,"factors")
##              Sepal.Length Sepal.Width Petal.Length Petal.Width
## Species                 0           0            0           0
## Sepal.Length            1           0            0           0
## Sepal.Width             0           1            0           0
## Petal.Length            0           0            1           0
## Petal.Width             0           0            0           1
## attr(,"term.labels")
## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width" 
## attr(,"order")
## [1] 1 1 1 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## attr(,"predvars")
## list(Species, Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)
## attr(,"dataClasses")
##      Species Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
##     "factor"    "numeric"    "numeric"    "numeric"    "numeric" 
## 
## $call
## lda(formula = Species ~ ., data = iris, CV = TRUE)
## 
## $xlevels
## named list()

head(r2$class)

## [1] setosa setosa setosa setosa setosa setosa
## Levels: setosa versicolor virginica

#the Maximum a Posteriori Probability (MAP) classification (a factor)
#posterior: posterior probabilities for the classes.
head(r2$posterior, 3)

##   setosa   versicolor    virginica
## 1      1 5.087494e-22 4.385241e-42
## 2      1 9.588256e-18 8.888069e-37
## 3      1 1.983745e-19 8.606982e-39

train <- sample(1:150, 75)
r3 <- lda(Species ~ ., # training model
          iris,
          prior = c(1,1,1)/3,
          subset = train)
plda = predict(object = r3, # predictions
               newdata = iris[-train, ])
head(plda$class)

## [1] setosa setosa setosa setosa setosa setosa
## Levels: setosa versicolor virginica

head(plda$posterior, 6) # posterior prob.

##    setosa   versicolor    virginica
## 6       1 3.209060e-20 2.483820e-38
## 7       1 8.120739e-18 1.075205e-35
## 9       1 4.370477e-15 1.013998e-32
## 10      1 1.683804e-18 1.605808e-37
## 13      1 2.294401e-18 2.152555e-37
## 14      1 4.506741e-19 3.002408e-38

head(plda$x, 3)

##        LD1        LD2
## 6 7.517248 -1.5730027
## 7 7.029720 -0.4482425
## 9 6.478778  0.8606600

plot(r)

plot(r3)

r <- lda(Species ~ .,
         iris,
         prior = c(1,1,1)/3)
prop.lda = r$svd^2/sum(r$svd^2)
plda <- predict(object = r,
                newdata = iris)
dataset = data.frame(species = iris[,"Species"],lda = plda$x)
ggplot(dataset) + geom_point(aes(lda.LD1, lda.LD2, colour = species, shape = species), size = 2.5) + labs(x = paste("LD1 (", percent(prop.lda[1]), ")", sep=""),y = paste("LD2 (", percent(prop.lda[2]), ")", sep=""))

#LDA is likely a good dimensionality reduction technique for this dataset, as it has been able to project the higher-dimensional data (four features: sepal length, sepal width, petal length, and petal width) onto a two-dimensional space (the plane of the scatter plot) while still maintaining some separability between the classes.
#The petal length appears to be a more important feature for classification than the sepal width, since the data points are more separated along the petal length axis.


# lets look at another way to divide a dataset

set.seed(101) # Nothing is random!!
sample_n(iris,10)

##    Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1           6.3         2.5          4.9         1.5 versicolor
## 2           6.3         3.3          4.7         1.6 versicolor
## 3           5.6         2.7          4.2         1.3 versicolor
## 4           6.5         3.0          5.2         2.0  virginica
## 5           5.0         2.0          3.5         1.0 versicolor
## 6           6.6         2.9          4.6         1.3 versicolor
## 7           5.1         2.5          3.0         1.1 versicolor
## 8           6.1         3.0          4.9         1.8  virginica
## 9           7.4         2.8          6.1         1.9  virginica
## 10          5.4         3.4          1.5         0.4     setosa

# Lets take a sample of 75/25 like before. Dplyr preserves class. 
training_sample <- sample(c(TRUE, FALSE), nrow(iris), replace = T, prob = c(0.75,0.25))
train <- iris[training_sample, ]
test <- iris[!training_sample, ]
#lets run LDA like before
lda.iris <- lda(Species ~ ., train)
# do a quick plot to understand how good the model is
plot(lda.iris, col = as.integer(train$Species))

# Sometime bell curves are better
plot(lda.iris, dimen = 1, type = "b")

# THis plot shows the essense of LDA. It puts everything on a line and finds cutoffs. 

#Here are some of the things that can be inferred from the confusion matrix:

#Out of 140 employees, 95 did not leave (no attrition) and 45 left (attrition).
#The model correctly predicted 90 out of the 95 employees who did not leave (no attrition). This is called the true negative rate.
#The model correctly predicted 25 out of the 45 employees who left (attrition). This is called the true positive rate.
#There were 5 false positives, which means that the model predicted that 5 employees would leave (attrition) when they actually did not.
#There were 10 false negatives, which means that the model predicted that 10 employees would not leave (no attrition) when they actually did leave (attrition).


# Partition plots
partimat(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data=train, method="lda")

# Lets focus on accuracy. Table function
lda.train <- predict(lda.iris)
train$lda <- lda.train$class
table(train$lda,train$Species)

##             
##              setosa versicolor virginica
##   setosa         35          0         0
##   versicolor      0         30         1
##   virginica       0          2        37

# running accuracy on the training set shows how good the model is. It is not an indication of "true" accuracy. We will use the test set to approximate accuracy
lda.test <- predict(lda.iris,test)
test$lda <- lda.test$class
table(test$lda,test$Species)

##             
##              setosa versicolor virginica
##   setosa         15          0         0
##   versicolor      0         18         0
##   virginica       0          0        12

# Wilk's Lambda and F test for each variablw
m <- manova(cbind(Sepal.Length,Sepal.Width,Petal.Length,Petal.Width)~Species,data=iris)
summary(m,test="Wilks")

##            Df    Wilks approx F num Df den Df    Pr(>F)    
## Species     2 0.023439   199.15      8    288 < 2.2e-16 ***
## Residuals 147                                              
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(m,test="Pillai")

##            Df Pillai approx F num Df den Df    Pr(>F)    
## Species     2 1.1919   53.466      8    290 < 2.2e-16 ***
## Residuals 147                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary.aov(m)

##  Response Sepal.Length :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Species       2 63.212  31.606  119.26 < 2.2e-16 ***
## Residuals   147 38.956   0.265                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Sepal.Width :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Species       2 11.345  5.6725   49.16 < 2.2e-16 ***
## Residuals   147 16.962  0.1154                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Petal.Length :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Species       2 437.10 218.551  1180.2 < 2.2e-16 ***
## Residuals   147  27.22   0.185                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Petal.Width :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Species       2 80.413  40.207  960.01 < 2.2e-16 ***
## Residuals   147  6.157   0.042                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Inference:

#Specifically, the plot shows three partition plots, each representing a different app error rate. The petal length and sepal width are on the x and y axes. The color regions correspond to the predicted class label for a given data point. In the top left plot, where the app error rate is 0.2, the data points in blue are classified as belonging to class 1, the green points are classified as class 2, and the yellow points are classified as class 3.

#From the plot, we can see that the model performs better when the petal length and sepal width are more distinct between the classes. In the top left plot (where the error rate is highest), the classes are more overlapping than in the bottom right plot (where the error rate is lowest). This suggests that the model is more confident in its predictions when the data points are clearly separated in terms of petal length and sepal width.